View Full Version : Observables in String Theory
Jack Tremarco
Aug22-04, 01:15 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Are there any known observables in string theory except for the\nS-matrix? Is the answer to this question the same whether we think of\nthe Polyakov string or some second-quantized approach like string\nfield theory or M-theory?\n\nThanks in advance!\n--Jack\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Are there any known observables in string theory except for the
S-matrix? Is the answer to this question the same whether we think of
the Polyakov string or some second-quantized approach like string
field theory or M-theory?
Thanks in advance!
--Jack
Jack Tremarco
Aug26-04, 01:39 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Is my question too difficult to answer, or is it not being take\nseriously? It is arguably not only a reasonable, but an important\nquestion.\n\nI found a partial answer in Gross\' and Erler\'s recent paper hep/th\n0406199. They say: "[...] in many theories of interest the only known\nobservables are S-matrix elements [...] it seems to be the case in\nstring theory, even open string theory".\n\nWhat about string field theory and M-theory? Any thoughts? Anyone?\n\n> Are there any known observables in string theory except for the\n> S-matrix? Is the answer to this question the same whether we think of\n> the Polyakov string or some second-quantized approach like string\n> field theory or M-theory?\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Is my question too difficult to answer, or is it not being take
seriously? It is arguably not only a reasonable, but an important
question.
I found a partial answer in Gross' and Erler's recent paper hep/th
0406199. They say: "[...] in many theories of interest the only known
observables are S-matrix elements [...] it seems to be the case in
string theory, even open string theory".
What about string field theory and M-theory? Any thoughts? Anyone?
> Are there any known observables in string theory except for the
> S-matrix? Is the answer to this question the same whether we think of
> the Polyakov string or some second-quantized approach like string
> field theory or M-theory?
Urs Schreiber
Aug26-04, 03:52 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Jack Tremarco" <jacktremarco@yahoo.com> schrieb im Newsbeitrag\nnews:5a4341f5.0408251705.5631d8c2-100000@posting.google.com...\n\n> > Are there any known observables in string theory except for the\n> > S-matrix? Is the answer to this question the same whether we think of\n> > the Polyakov string or some second-quantized approach like string\n> > field theory or M-theory?\n\n> Is my question too difficult to answer, or is it not being take\n> seriously? It is arguably not only a reasonable, but an important\n> question.\n>\n> I found a partial answer in Gross\' and Erler\'s recent paper hep/th\n> 0406199. They say: "[...] in many theories of interest the only known\n> observables are S-matrix elements [...] it seems to be the case in\n> string theory, even open string theory".\n>\n> What about string field theory and M-theory? Any thoughts? Anyone?\n\nMinds greater than mine will have to help you here, but I can at least make\nsome vague comments which might make somebody more knowledgable than me feel\nuncomfortable enough with to set us straight.\n\nConcerning purely open string field theory: As was mentioned in a recent\nthread this can be rewritten (unless I am overlooking some subtlety) as a\nfield theory for point particles (a non-local one with infinitely many\ninteracting fields in it). So I would guess that any observable admissable\nin standard field theory would give us an observable for open string field\ntheory using this formulation.\n\nBut open string field theory does not contain gravity and maybe the need to\nswitch to the S-matrix only is ultimately related to gravity. This is at\nleast what seems to be suggested by AdS/CFT, where the correlators on the\nboundary of a gravitational system contain at the same time all the\ninformation of that bulk gravitational system.\n\nThis is also the argument Polchinski gives on p. 104 of the first volume of\nhis book, where it says\n\n"Second, string theory contains gravity, and in general relativity simple\noff-shell amplitudes do not exist. This is because we have to specify the\nlocation of the probe, but the coordinates are unphysical and\ncoordinate-invariant off-shell amplitudes are much more complicated. Third,\nin string theory we don not have the freedom to introduce additional fields\nto measure local observables (analogous to the way electroweak processes are\nused to probe strongly interacting systems): we must use the strings\nthemselves, or other objects that we will discuss (D-branes and solitons)\nthat are intrinsic to the theory."\n\nSo when you ask about string field theory one should really be thinking of\nclosed string field theory, which remains only piecewise defined.\n\n(BTW \'t Hooft is speculating that there is some deep connection between\nholography, the S-matrix and the statistical nature of quantum mechanics:\nhttp://golem.ph.utexas.edu/string/archives/000400.html)\n\nConcerning Matrix theory proposals for M-theory: This gives us a quantum\nmechanical system of a large number but of finitely many degrees of freedom,\nwhich is supposed to give the nonperturbative description of M-theory for\ngiven asymptotic boundary conditions. Naively it would appear to me that\nhence the observables in Matrix theory are those constructible by the\nstandard rules of quantum mechanics. For instance the transversal "position"\nof the n-th D0 brane (really the n-th diagonal entry of the matrices) should\nbe such an observable I\'d think, or maybe the exponential of the imaginary\nunit times this operator, if you are worried about unbounded operators.\n\nI don\'t know if this has to do with any S-matrix. Wouldn\'t surprise me,\nthough, if for instance all these observables in Matrix Theory can be shown\nto compute S-matrix elements in the perturbative string theory description\nof the same system, or something like that. But I am way out of my depth and\njust speculating.\n\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Jack Tremarco" <jacktremarco@yahoo.com> schrieb im Newsbeitrag
news:5a4341f5.0408251705.5631d8c2-100000@posting.google.com...
> > Are there any known observables in string theory except for the
> > S-matrix? Is the answer to this question the same whether we think of
> > the Polyakov string or some second-quantized approach like string
> > field theory or M-theory?
> Is my question too difficult to answer, or is it not being take
> seriously? It is arguably not only a reasonable, but an important
> question.
>
> I found a partial answer in Gross' and Erler's recent paper hep/th
> 0406199. They say: "[...] in many theories of interest the only known
> observables are S-matrix elements [...] it seems to be the case in
> string theory, even open string theory".
>
> What about string field theory and M-theory? Any thoughts? Anyone?
Minds greater than mine will have to help you here, but I can at least make
some vague comments which might make somebody more knowledgable than me feel
uncomfortable enough with to set us straight.
Concerning purely open string field theory: As was mentioned in a recent
thread this can be rewritten (unless I am overlooking some subtlety) as a
field theory for point particles (a non-local one with infinitely many
interacting fields in it). So I would guess that any observable admissable
in standard field theory would give us an observable for open string field
theory using this formulation.
But open string field theory does not contain gravity and maybe the need to
switch to the S-matrix only is ultimately related to gravity. This is at
least what seems to be suggested by AdS/CFT, where the correlators on the
boundary of a gravitational system contain at the same time all the
information of that bulk gravitational system.
This is also the argument Polchinski gives on p. 104 of the first volume of
his book, where it says
"Second, string theory contains gravity, and in general relativity simple
off-shell amplitudes do not exist. This is because we have to specify the
location of the probe, but the coordinates are unphysical and
coordinate-invariant off-shell amplitudes are much more complicated. Third,
in string theory we don not have the freedom to introduce additional fields
to measure local observables (analogous to the way electroweak processes are
used to probe strongly interacting systems): we must use the strings
themselves, or other objects that we will discuss (D-branes and solitons)
that are intrinsic to the theory."
So when you ask about string field theory one should really be thinking of
closed string field theory, which remains only piecewise defined.
(BTW 't Hooft is speculating that there is some deep connection between
holography, the S-matrix and the statistical nature of quantum mechanics:
http://golem.ph.utexas.edu/string/archives/000400.html)
Concerning Matrix theory proposals for M-theory: This gives us a quantum
mechanical system of a large number but of finitely many degrees of freedom,
which is supposed to give the nonperturbative description of M-theory for
given asymptotic boundary conditions. Naively it would appear to me that
hence the observables in Matrix theory are those constructible by the
standard rules of quantum mechanics. For instance the transversal "position"
of the n-th D0 brane (really the n-th diagonal entry of the matrices) should
be such an observable I'd think, or maybe the exponential of the imaginary
unit times this operator, if you are worried about unbounded operators.
I don't know if this has to do with any S-matrix. Wouldn't surprise me,
though, if for instance all these observables in Matrix Theory can be shown
to compute S-matrix elements in the perturbative string theory description
of the same system, or something like that. But I am way out of my depth and
just speculating.
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Jack Tremarco <jacktremarco@yahoo.com> wrote:\n\nThis may be more simplistic than what youre looking for,\nBut I thought momentum, Mass etc are all observables in\n1-string string theory. Now in many-string string theory\nwhich I think String Field Theory is a version of, I don\'t\nknow what are observables and what are not. I feel however\nthat the situation is similar to observables in 1 particle theory\nV.S. observables in qft. Also it\'s important to state one\'s\ndefinition of observables, i.e., are you talking about operators,\nor are you using the word to mean something more like what\'s\npractical or measurable in the lab.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Jack Tremarco <jacktremarco@yahoo.com> wrote:
This may be more simplistic than what youre looking for,
But I thought momentum, Mass etc are all observables in
1-string string theory. Now in many-string string theory
which I think String Field Theory is a version of, I don't
know what are observables and what are not. I feel however
that the situation is similar to observables in 1 particle theory
V.S. observables in qft. Also it's important to state one's
definition of observables, i.e., are you talking about operators,
or are you using the word to mean something more like what's
practical or measurable in the lab.
Jack Tremarco
Aug27-04, 08:24 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>> This may be more simplistic than what youre looking for,\n> But I thought momentum, Mass etc are all observables in\n> 1-string string theory.\n\nLocal observables such as energy density are problematic in\ngravitational theories because they are not diffeomorphism invariant.\nYou can make a simple physical argument based on time-energy\nuncertainty to see the physical origin: The measurement will either\ntake place on a time scale on which the geometry evolves considerably,\nor it will necessarily disturb the quantity of interest. The result is\nfuzzy in either case.\n\nS-matrix elements do not appear to explain certain things. How can you\nexpress what an observer who falls into a black hole sees in terms of\nthem? The S-matrix is insufficient to probe microscopic causality. But\nstring theory should preserve some sense of locality if it is to\ndescribe nature as we see it.\n\n> Now in many-string string theory\n> which I think String Field Theory is a version of, I don\'t\n> know what are observables and what are not. I feel however\n> that the situation is similar to observables in 1 particle theory\n> V.S. observables in qft. Also it\'s important to state one\'s\n> definition of observables, i.e., are you talking about operators,\n> or are you using the word to mean something more like what\'s\n> practical or measurable in the lab.\n\nObservables are quantities that can be assigned an immediate physical\nmeaning, that is, they can be measured in principle. Since the dawn of\nquantum theory the question for the role of observables has caused a\ngreat deal of confusion. And apparently it\'s not over yet...\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>> This may be more simplistic than what youre looking for,
> But I thought momentum, Mass etc are all observables in
> 1-string string theory.
Local observables such as energy density are problematic in
gravitational theories because they are not diffeomorphism invariant.
You can make a simple physical argument based on time-energy
uncertainty to see the physical origin: The measurement will either
take place on a time scale on which the geometry evolves considerably,
or it will necessarily disturb the quantity of interest. The result is
fuzzy in either case.
S-matrix elements do not appear to explain certain things. How can you
express what an observer who falls into a black hole sees in terms of
them? The S-matrix is insufficient to probe microscopic causality. But
string theory should preserve some sense of locality if it is to
describe nature as we see it.
> Now in many-string string theory
> which I think String Field Theory is a version of, I don't
> know what are observables and what are not. I feel however
> that the situation is similar to observables in 1 particle theory
> V.S. observables in qft. Also it's important to state one's
> definition of observables, i.e., are you talking about operators,
> or are you using the word to mean something more like what's
> practical or measurable in the lab.
Observables are quantities that can be assigned an immediate physical
meaning, that is, they can be measured in principle. Since the dawn of
quantum theory the question for the role of observables has caused a
great deal of confusion. And apparently it's not over yet...
Arvind Rajaraman
Aug27-04, 12:51 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hi Jack,\n\nFor string theory in flat space, the only known observable is the\nS-matrix. For string theory in asymptotically anti-de-Sitter space, the\nobservables are correlation functions in Yang-Mills theory (as in the\nAdS/CFT correspondence.) For de Sitter space, nobody knows (though see\nWitten\'s paper hep-th/0106109.)\n\nIt is possible to reconstruct quasi-local observables from an S-matrix,\nsince the S-matrix contains all the scattering information. So that\'s not\nthe problem.\n\nArvind.\n\nOn Thu, 26 Aug 2004, Jack Tremarco wrote:\n\n> Is my question too difficult to answer, or is it not being take\n> seriously? It is arguably not only a reasonable, but an important\n> question.\n>\n> I found a partial answer in Gross\' and Erler\'s recent paper hep/th\n> 0406199. They say: "[...] in many theories of interest the only known\n> observables are S-matrix elements [...] it seems to be the case in\n> string theory, even open string theory".\n>\n> What about string field theory and M-theory? Any thoughts? Anyone?\n>\n> > Are there any known observables in string theory except for the\n> > S-matrix? Is the answer to this question the same whether we think of\n> > the Polyakov string or some second-quantized approach like string\n> > field theory or M-theory?\n>\n>\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hi Jack,
For string theory in flat space, the only known observable is the
S-matrix. For string theory in asymptotically anti-de-Sitter space, the
observables are correlation functions in Yang-Mills theory (as in the
AdS/CFT correspondence.) For de Sitter space, nobody knows (though see
Witten's paper http://www.arxiv.org/abs/hep-th/0106109.)
It is possible to reconstruct quasi-local observables from an S-matrix,
since the S-matrix contains all the scattering information. So that's not
the problem.
Arvind.
On Thu, 26 Aug 2004, Jack Tremarco wrote:
> Is my question too difficult to answer, or is it not being take
> seriously? It is arguably not only a reasonable, but an important
> question.
>
> I found a partial answer in Gross' and Erler's recent paper hep/th
> 0406199. They say: "[...] in many theories of interest the only known
> observables are S-matrix elements [...] it seems to be the case in
> string theory, even open string theory".
>
> What about string field theory and M-theory? Any thoughts? Anyone?
>
> > Are there any known observables in string theory except for the
> > S-matrix? Is the answer to this question the same whether we think of
> > the Polyakov string or some second-quantized approach like string
> > field theory or M-theory?
>
>
Urs Schreiber
Aug30-04, 05:16 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Arvind Rajaraman" <arajaram@uci.edu> schrieb im Newsbeitrag\nnews:Pine.LNX.4.31.0408271344120.7917-100000@feynman.harvard.edu...\n\n> For string theory in flat space, the only known observable is the\n> S-matrix. For string theory in asymptotically anti-de-Sitter space, the\n> observables are correlation functions in Yang-Mills theory (as in the\n> AdS/CFT correspondence.) For de Sitter space, nobody knows (though see\n> Witten\'s paper hep-th/0106109.)\n>\n> It is possible to reconstruct quasi-local observables from an S-matrix,\n> since the S-matrix contains all the scattering information. So that\'s not\n> the problem.\n\nCan one construct a mapping between S-matrix elements and observables in\nMatrix Theory?\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Arvind Rajaraman" <arajaram@uci.edu> schrieb im Newsbeitrag
news:Pine.LNX.4.31.0408271344120.7917-100000@feynman.harvard.edu...
> For string theory in flat space, the only known observable is the
> S-matrix. For string theory in asymptotically anti-de-Sitter space, the
> observables are correlation functions in Yang-Mills theory (as in the
> AdS/CFT correspondence.) For de Sitter space, nobody knows (though see
> Witten's paper http://www.arxiv.org/abs/hep-th/0106109.)
>
> It is possible to reconstruct quasi-local observables from an S-matrix,
> since the S-matrix contains all the scattering information. So that's not
> the problem.
Can one construct a mapping between S-matrix elements and observables in
Matrix Theory?
Ted Erler
Aug31-04, 03:42 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Jack Tremarco <jacktremarco@yahoo.com> wrote in message news:<5a4341f5.0408251705.5631d8c2-100000@posting.google.com>...\n> Is my question too difficult to answer, or is it not being take\n> seriously? It is arguably not only a reasonable, but an important\n> question.\n>\n> I found a partial answer in Gross\' and Erler\'s recent paper hep/th\n> 0406199. They say: "[...] in many theories of interest the only known\n> observables are S-matrix elements [...] it seems to be the case in\n> string theory, even open string theory".\n>\n> What about string field theory and M-theory? Any thoughts? Anyone?\n>\n> > Are there any known observables in string theory except for the\n> > S-matrix? Is the answer to this question the same whether we think of\n> > the Polyakov string or some second-quantized approach like string\n> > field theory or M-theory?\n\nThe whole question of "observables" and their interpretation in gauge\ntheories is an old and often confusing question.\n\nTake for example electromagnatism. If you completely fix a gauge, e.g.\nA_0=0, the remaining three components A_i are physical\nobservables---they are well-defined functions of the field strength F.\nHowever, the physical interpretation of the A_is in this particular\ngauge is somewhat preverse, and ordinarily we do not think of them as\nbeing the quantities we measure in a simple experiment. Hence,\nformally they are obsevables, but they are not things we ordinarily\nthink of observing.\n\nThis example is quite analogous to string theory in lightcone gauge.\nIn lightcone string field theory, the gauge has been completely fixed,\nand because of that the string field *itself* is a physical\nobservable---one that is not obviously equivalent to the S-matrix.\nHowever, the physical interpretation of the lightcone string field, in\nterms of simple measurements, seems obscure.\n\nWhen we said in our paper, "[...] in many theories of interest the\nonly known observables are S-matrix elements,\'\' what we meant really\nis that the S-matrix is the only observable we know how to (in\nprinciple) measure, calculate, and physically interpret. Hopefully,\nthe S-matrix is not the only observable in string theory since there\nare many physical questions we would like to ask which are beyond the\nS-matrix\'s capacity to answer.\n\nThat being said, the second quantized operator formalism we\nconstructed in our paper provides a partial (and perhaps not completly\nsatisfying) answer to your question. Roughly speaking, observables in\nstring theory correspond to matrix elements of physical operators\nbetween physical states, where "physical" means that they lie in the\nappropriate BRST cohomology classes of the (spacetime) BRST operator\nat ghost number 0. These include, for example, finite (lightcone) time\ntransition amplitudes between physical states, since the Hamiltonian\nitself is a physical operator. This formalism was constructed for open\nstring field theory, but since it is quantum mechanical it ought to\ninclude closed strings as well. In principle we can ask physical\nquestions which are beyond the S-matrix in this formalsim, for\nexample, "If I start in a vacuum represented by the physical state\n|\\Psi_1>, what is the probability per time that I will tunnell to the\nvacuum represented by the physical state |\\Psi_2>?" Of course, I don\'t\nhave nearly sufficeint understanding or control of the formalism to\nreally calculate the answer to this type of question, but at least it\nseems well-posed in this framework.\n\nOf course, actually interpreting these observables in our formalism is\nan emmense challenge, as they are defined formally as equivalence\nclasses in a huge space of unphysical ghost degrees of freedom.\nHowever, at least our paper gives some insight into the nature of\nthese observables: they are well-defined and local in lightcone time.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Jack Tremarco <jacktremarco@yahoo.com> wrote in message news:<5a4341f5.0408251705.5631d8c2-100000@posting.google.com>...
> Is my question too difficult to answer, or is it not being take
> seriously? It is arguably not only a reasonable, but an important
> question.
>
> I found a partial answer in Gross' and Erler's recent paper hep/th
> 0406199. They say: "[...] in many theories of interest the only known
> observables are S-matrix elements [...] it seems to be the case in
> string theory, even open string theory".
>
> What about string field theory and M-theory? Any thoughts? Anyone?
>
> > Are there any known observables in string theory except for the
> > S-matrix? Is the answer to this question the same whether we think of
> > the Polyakov string or some second-quantized approach like string
> > field theory or M-theory?
The whole question of "observables" and their interpretation in gauge
theories is an old and often confusing question.
Take for example electromagnatism. If you completely fix a gauge, e.g.
A_0=0, the remaining three components A_i are physical
observables---they are well-defined functions of the field strength F.
However, the physical interpretation of the A_{is} in this particular
gauge is somewhat preverse, and ordinarily we do not think of them as
being the quantities we measure in a simple experiment. Hence,
formally they are obsevables, but they are not things we ordinarily
think of observing.
This example is quite analogous to string theory in lightcone gauge.
In lightcone string field theory, the gauge has been completely fixed,
and because of that the string field *itself* is a physical
observable---one that is not obviously equivalent to the S-matrix.
However, the physical interpretation of the lightcone string field, in
terms of simple measurements, seems obscure.
When we said in our paper, "[...] in many theories of interest the
only known observables are S-matrix elements,'' what we meant really
is that the S-matrix is the only observable we know how to (in
principle) measure, calculate, and physically interpret. Hopefully,
the S-matrix is not the only observable in string theory since there
are many physical questions we would like to ask which are beyond the
S-matrix's capacity to answer.
That being said, the second quantized operator formalism we
constructed in our paper provides a partial (and perhaps not completly
satisfying) answer to your question. Roughly speaking, observables in
string theory correspond to matrix elements of physical operators
between physical states, where "physical" means that they lie in the
appropriate BRST cohomology classes of the (spacetime) BRST operator
at ghost number . These include, for example, finite (lightcone) time
transition amplitudes between physical states, since the Hamiltonian
itself is a physical operator. This formalism was constructed for open
string field theory, but since it is quantum mechanical it ought to
include closed strings as well. In principle we can ask physical
questions which are beyond the S-matrix in this formalsim, for
example, "If I start in a vacuum represented by the physical state
|\Psi_1>, what is the probability per time that I will tunnell to the
vacuum represented by the physical state |\Psi_2>?" Of course, I don't
have nearly sufficeint understanding or control of the formalism to
really calculate the answer to this type of question, but at least it
seems well-posed in this framework.
Of course, actually interpreting these observables in our formalism is
an emmense challenge, as they are defined formally as equivalence
classes in a huge space of unphysical ghost degrees of freedom.
However, at least our paper gives some insight into the nature of
these observables: they are well-defined and local in lightcone time.
Arvind Rajaraman
Sep1-04, 12:21 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Mon, 30 Aug 2004, Urs Schreiber wrote:\n\n> "Arvind Rajaraman" <arajaram@uci.edu> schrieb im Newsbeitrag\n> news:Pine.LNX.4.31.0408271344120.7917-100000@feynman.harvard.edu...\n>\n> > For string theory in flat space, the only known observable is the\n> > S-matrix. For string theory in asymptotically anti-de-Sitter space, the\n> > observables are correlation functions in Yang-Mills theory (as in the\n> > AdS/CFT correspondence.) For de Sitter space, nobody knows (though see\n> > Witten\'s paper hep-th/0106109.)\n> >\n> > It is possible to reconstruct quasi-local observables from an S-matrix,\n> > since the S-matrix contains all the scattering information. So that\'s not\n> > the problem.\n>\n> Can one construct a mapping between S-matrix elements and observables in\n> Matrix Theory?\n>\n\nThere are observables in Matrix-theory which correspond to the S-matrix of\ngravitons. Specifically, we consider the asymptotic states to be the\nmarginally bound states of N D0-branes, which are mapped to gravitons with\nN units of lightcone momentum. The S-matrix for these objects can then be\ncomputed within the gauge theory. So there is an onto mapping from the\nobservables of matrix theory to the S-matrix.\n\nI do not know if there are extra observables in Matrix theory which do not\ncorrespond to anything in the S-matrix. I would assume not, but I don\'t\nknow for sure.\n\nArvind.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Mon, 30 Aug 2004, Urs Schreiber wrote:
> "Arvind Rajaraman" <arajaram@uci.edu> schrieb im Newsbeitrag
> news:Pine.LNX.4.31.0408271344120.7917-100000@feynman.harvard.edu...
>
> > For string theory in flat space, the only known observable is the
> > S-matrix. For string theory in asymptotically anti-de-Sitter space, the
> > observables are correlation functions in Yang-Mills theory (as in the
> > AdS/CFT correspondence.) For de Sitter space, nobody knows (though see
> > Witten's paper http://www.arxiv.org/abs/hep-th/0106109.)
> >
> > It is possible to reconstruct quasi-local observables from an S-matrix,
> > since the S-matrix contains all the scattering information. So that's not
> > the problem.
>
> Can one construct a mapping between S-matrix elements and observables in
> Matrix Theory?
>
There are observables in Matrix-theory which correspond to the S-matrix of
gravitons. Specifically, we consider the asymptotic states to be the
marginally bound states of N D0-branes, which are mapped to gravitons with
N units of lightcone momentum. The S-matrix for these objects can then be
computed within the gauge theory. So there is an onto mapping from the
observables of matrix theory to the S-matrix.
I do not know if there are extra observables in Matrix theory which do not
correspond to anything in the S-matrix. I would assume not, but I don't
know for sure.
Arvind.
Lubos Motl
Sep2-04, 10:25 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Wed, 1 Sep 2004, Arvind Rajaraman wrote:\n\n> I do not know if there are extra observables in Matrix theory which do not\n> correspond to anything in the S-matrix. I would assume not, but I don\'t\n> know for sure.\n\nHi Arvind, is not it clear that there are? In Matrix theory, you can\nconstruct a state at the light-cone time X^+, and evolve it to another\ntime Y^+. It\'s a finite time evolution, and there should be a finite time\nevolution operator, inherited from quantum mechanics - well, BFSS *is*\nquantum mechanics. Well, it is an operator relating states of Matrix\ntheory - whose relation to well-known graviton scattering states is not\nstraightforward, especially if the state contains a couple of gravitons\nseparated by finite distances. Nevertheless all these non-asymptotic\nstates seem to exist in Matrix theory, including the amplitudes for their\nfinite light-cone time evolution. Although these are heavily\nLorentz-breaking states and observables, they seem to be gauge-invariant\nand physical.\n\nDo you agree with the comments above? Do you think that these finite-time\namplitudes, apparently present in Matrix theory, can be (uniquely?)\nreconstructed from the S-matrix which only involves the infinite-time\nevolution? Tx, Lubos\n___________________________________________ ___________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 1 Sep 2004, Arvind Rajaraman wrote:
> I do not know if there are extra observables in Matrix theory which do not
> correspond to anything in the S-matrix. I would assume not, but I don't
> know for sure.
Hi Arvind, is not it clear that there are? In Matrix theory, you can
construct a state at the light-cone time X^+, and evolve it to another
time Y^+. It's a finite time evolution, and there should be a finite time
evolution operator, inherited from quantum mechanics - well, BFSS *is*
quantum mechanics. Well, it is an operator relating states of Matrix
theory - whose relation to well-known graviton scattering states is not
straightforward, especially if the state contains a couple of gravitons
separated by finite distances. Nevertheless all these non-asymptotic
states seem to exist in Matrix theory, including the amplitudes for their
finite light-cone time evolution. Although these are heavily
Lorentz-breaking states and observables, they seem to be gauge-invariant
and physical.
Do you agree with the comments above? Do you think that these finite-time
amplitudes, apparently present in Matrix theory, can be (uniquely?)
reconstructed from the S-matrix which only involves the infinite-time
evolution? Tx, Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Urs Schreiber
Sep4-04, 10:06 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nHi Lubos,\n\nOn Thu, 2 Sep 2004, Lubos Motl wrote:\n\n> On Wed, 1 Sep 2004, Arvind Rajaraman wrote:\n>\n> > I do not know if there are extra observables in Matrix theory which do not\n> > correspond to anything in the S-matrix. I would assume not, but I don\'t\n> > know for sure.\n>\n> Hi Arvind, is not it clear that there are? In Matrix theory, you can\n> construct a state at the light-cone time X^+, and evolve it to another\n> time Y^+. It\'s a finite time evolution, and there should be a finite time\n> evolution operator, inherited from quantum mechanics - well, BFSS *is*\n> quantum mechanics. Well, it is an operator relating states of Matrix\n> theory - whose relation to well-known graviton scattering states is not\n> straightforward, especially if the state contains a couple of gravitons\n> separated by finite distances. Nevertheless all these non-asymptotic\n> states seem to exist in Matrix theory, including the amplitudes for their\n> finite light-cone time evolution. Although these are heavily\n> Lorentz-breaking states and observables, they seem to be gauge-invariant\n> and physical.\n>\n> Do you agree with the comments above? Do you think that these finite-time\n> amplitudes, apparently present in Matrix theory, can be (uniquely?)\n> reconstructed from the S-matrix which only involves the infinite-time\n> evolution? Tx, Lubos\n\nI agree with all your comments. It does seem clear that Matrix theory has\nmore observables, and I did think of that when writing the previous post.\nBut perhaps in light cone gauge, there is a way to derive these objects\nfrom the S-matrix.\n\nIf we interpret this in DLCQ M-theory, finite time correlations appear to\ncorrespond in spacetime to the amplitude for a D0 brane to evolve from\npoint X to point Y. At finite string coupling, we would certainly think of\nthis as being not-gauge invariant. But in the DLCQ limit, the D-branes are\ninfinitely massive, and the finite time correlation function should be a\ngauge invariant quantity derivable from the S-matrix (the D-branes are\nclassical in this limit.)\n\nI don\'t know if this really makes sense, though. What do you think?\n\nArvind.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hi Lubos,
On Thu, 2 Sep 2004, Lubos Motl wrote:
> On Wed, 1 Sep 2004, Arvind Rajaraman wrote:
>
> > I do not know if there are extra observables in Matrix theory which do not
> > correspond to anything in the S-matrix. I would assume not, but I don't
> > know for sure.
>
> Hi Arvind, is not it clear that there are? In Matrix theory, you can
> construct a state at the light-cone time X^+, and evolve it to another
> time Y^+. It's a finite time evolution, and there should be a finite time
> evolution operator, inherited from quantum mechanics - well, BFSS *is*
> quantum mechanics. Well, it is an operator relating states of Matrix
> theory - whose relation to well-known graviton scattering states is not
> straightforward, especially if the state contains a couple of gravitons
> separated by finite distances. Nevertheless all these non-asymptotic
> states seem to exist in Matrix theory, including the amplitudes for their
> finite light-cone time evolution. Although these are heavily
> Lorentz-breaking states and observables, they seem to be gauge-invariant
> and physical.
>
> Do you agree with the comments above? Do you think that these finite-time
> amplitudes, apparently present in Matrix theory, can be (uniquely?)
> reconstructed from the S-matrix which only involves the infinite-time
> evolution? Tx, Lubos
I agree with all your comments. It does seem clear that Matrix theory has
more observables, and I did think of that when writing the previous post.
But perhaps in light cone gauge, there is a way to derive these objects
from the S-matrix.
If we interpret this in DLCQ M-theory, finite time correlations appear to
correspond in spacetime to the amplitude for a D0 brane to evolve from
point X to point Y. At finite string coupling, we would certainly think of
this as being not-gauge invariant. But in the DLCQ limit, the D-branes are
infinitely massive, and the finite time correlation function should be a
gauge invariant quantity derivable from the S-matrix (the D-branes are
classical in this limit.)
I don't know if this really makes sense, though. What do you think?
Arvind.
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