View Full Version : nonlinearities in QFT
Blake Winter
Sep24-04, 08:12 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>I was reading a few more papers on arxiv.org:\nhttp://www.arxiv.org/abs/quant-ph/0003083\nhttp://www.arxiv.org/abs/quant-ph/0006079\n\nIn the first paper Johan Hansson proposes that perhaps the\nnonlinearities inherent in the nonabelian parts of the standard model\nare responsible for the "collapse" of the wavefunction (which would\nthen, it seems, actually be a deterministic yet nonlinear and\ntherefore unpredictable occurance). He suggests in the second paper a\npossible way to test this; the basic experimental setup is based on\nthe setups used to detect a chaotic attractor in a dripping water\nfaucets. He suggests using a small radioactive source and measure the\ndecay times.\nBut it seems that this won\'t work to me; this would be like trying to\nfind an attractor in the drip times for lots of seperate water faucets\neach of which only drips once. The only way this would be a good test\nwould be if the nonlinear collapse of the part of the wavefunction\nwhich governs one atom also caused the collapse of all the other\natoms. Otherwise, the decay time of one won\'t affect the other, so I\ndon\'t think we would find an attractor even if his theory were\ncorrect.\nDoes anyone else have any ideas on whether this would be a valid test?\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>I was reading a few more papers on arxiv.org:
http://www.arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/0003083
http://www.arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/0006079
In the first paper Johan Hansson proposes that perhaps the
nonlinearities inherent in the nonabelian parts of the standard model
are responsible for the "collapse" of the wavefunction (which would
then, it seems, actually be a deterministic yet nonlinear and
therefore unpredictable occurance). He suggests in the second paper a
possible way to test this; the basic experimental setup is based on
the setups used to detect a chaotic attractor in a dripping water
faucets. He suggests using a small radioactive source and measure the
decay times.
But it seems that this won't work to me; this would be like trying to
find an attractor in the drip times for lots of seperate water faucets
each of which only drips once. The only way this would be a good test
would be if the nonlinear collapse of the part of the wavefunction
which governs one atom also caused the collapse of all the other
atoms. Otherwise, the decay time of one won't affect the other, so I
don't think we would find an attractor even if his theory were
correct.
Does anyone else have any ideas on whether this would be a valid test?
Arnold Neumaier
Sep25-04, 05:03 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>Blake Winter wrote:\n> I was reading a few more papers on arxiv.org:\n> http://www.arxiv.org/abs/quant-ph/0003083\n> http://www.arxiv.org/abs/quant-ph/0006079\n>\n> In the first paper Johan Hansson proposes that perhaps the\n> nonlinearities inherent in the nonabelian parts of the standard model\n> are responsible for the "collapse" of the wavefunction (which would\n> then, it seems, actually be a deterministic yet nonlinear and\n> therefore unpredictable occurance).\n\nThe first article says:\n\'\'The nonabelian vector gauge fields are governed by a set of coupled,\nsecond order, nonlinear PDEs on Minkowski spacetime.\'\'\nClearly, this mistakes the classical nonlinear dynamics of nonabelian\ngauge fields for nonlinear quantum dynamics. But relativistic QFT does\nnot give a well-defined dynamics at all; all it defines is an S-matrix.\nSo the article is void.\n\nOn the other hand, it is quite possible that a solution of the unresolved\nissues in relativistic QFT are related to the unresolved issues in\nquantum measurement theory.\n\n\nArnold Neumaier\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>Blake Winter wrote:
> I was reading a few more papers on arxiv.org:
> http://www.arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/0003083
> http://www.arxiv.org/abs/http://www.arxiv.org/abs/quant-ph/0006079
>
> In the first paper Johan Hansson proposes that perhaps the
> nonlinearities inherent in the nonabelian parts of the standard model
> are responsible for the "collapse" of the wavefunction (which would
> then, it seems, actually be a deterministic yet nonlinear and
> therefore unpredictable occurance).
The first article says:
''The nonabelian vector gauge fields are governed by a set of coupled,
second order, nonlinear PDEs on Minkowski spacetime.''
Clearly, this mistakes the classical nonlinear dynamics of nonabelian
gauge fields for nonlinear quantum dynamics. But relativistic QFT does
not give a well-defined dynamics at all; all it defines is an S-matrix.
So the article is void.
On the other hand, it is quite possible that a solution of the unresolved
issues in relativistic QFT are related to the unresolved issues in
quantum measurement theory.
Arnold Neumaier
Blake Winter
Sep27-04, 03:31 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>\n\n\n> On the other hand, it is quite possible that a solution of the unresolved\n> issues in relativistic QFT are related to the unresolved issues in\n> quantum measurement theory.\n>\n>\n> Arnold Neumaier\n\nThanks. As you can tell I am not all that knowledgeable about QFT.\nIf you don\'t mind, could you elaborate a bit on what issues you are\ntalking about in QFT?\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 the other hand, it is quite possible that a solution of the unresolved
> issues in relativistic QFT are related to the unresolved issues in
> quantum measurement theory.
>
>
> Arnold Neumaier
Thanks. As you can tell I am not all that knowledgeable about QFT.
If you don't mind, could you elaborate a bit on what issues you are
talking about in QFT?
Blake Winter
Sep27-04, 10:20 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>\n\n\n> The first article says:\n> \'\'The nonabelian vector gauge fields are governed by a set of coupled,\n> second order, nonlinear PDEs on Minkowski spacetime.\'\'\n> Clearly, this mistakes the classical nonlinear dynamics of nonabelian\n> gauge fields for nonlinear quantum dynamics. But relativistic QFT does\n> not give a well-defined dynamics at all; all it defines is an S-matrix.\n> So the article is void.\n\n\nI might add to my earlier questions, does this mean that in QFT we\ncan\'t start with some Psi describing the state of our fields at t = 0\nand evolve it forward in time via d/dt Psi = H Psi, or some other such\nequation?\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>The first article says:
> ''The nonabelian vector gauge fields are governed by a set of coupled,
> second order, nonlinear PDEs on Minkowski spacetime.''
> Clearly, this mistakes the classical nonlinear dynamics of nonabelian
> gauge fields for nonlinear quantum dynamics. But relativistic QFT does
> not give a well-defined dynamics at all; all it defines is an S-matrix.
> So the article is void.
I might add to my earlier questions, does this mean that in QFT we
can't start with some \Psi describing the state of our fields at t =
and evolve it forward in time via d/dt \Psi = H \Psi, or some other such
equation?
Arnold Neumaier
Sep27-04, 10:20 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>\n\nBlake Winter wrote:\n>>On the other hand, it is quite possible that a solution of the unresolved\n>>issues in relativistic QFT are related to the unresolved issues in\n>>quantum measurement theory.\n>>\n>>Arnold Neumaier\n>\n> Thanks. As you can tell I am not all that knowledgeable about QFT.\n> If you don\'t mind, could you elaborate a bit on what issues you are\n> talking about in QFT?\n\nThe standard theory gives an S-matrix (or rather an asymptotic series\nfor it) but not a dynamics at finite times. Clearly, measurements happen\nin finite time, hence cannot be described at present in a fundamental way\n(i.e., beyond the nonrelativistic QM approximation). Thus foundational\nstudies based on nonrelativistic QM are naturally incomplete.\n\n\nArnold Neumaier\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>Blake Winter wrote:
>>On the other hand, it is quite possible that a solution of the unresolved
>>issues in relativistic QFT are related to the unresolved issues in
>>quantum measurement theory.
>>
>>Arnold Neumaier
>
> Thanks. As you can tell I am not all that knowledgeable about QFT.
> If you don't mind, could you elaborate a bit on what issues you are
> talking about in QFT?
The standard theory gives an S-matrix (or rather an asymptotic series
for it) but not a dynamics at finite times. Clearly, measurements happen
in finite time, hence cannot be described at present in a fundamental way
(i.e., beyond the nonrelativistic QM approximation). Thus foundational
studies based on nonrelativistic QM are naturally incomplete.
Arnold Neumaier
Blake Winter
Sep28-04, 02:28 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>But don\'t we see LQG attempting to evolve from one spin foam as a\nstarting point to another? And can\'t we use path integrals to evolve\nfrom one field configuration to another? Then by starting with some\nPsi over the initial configurations we will be able to evolve it in\ntime, right? I guess I\'m wondering why its not true that the dynamics\nare properly defined.\nI hope this makes sense - I\'m learning about QFT as much as I can in\nmy spare time but this question may be "not even wrong".\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>But don't we see LQG attempting to evolve from one spin foam as a
starting point to another? And can't we use path integrals to evolve
from one field configuration to another? Then by starting with some
\Psi over the initial configurations we will be able to evolve it in
time, right? I guess I'm wondering why its not true that the dynamics
are properly defined.
I hope this makes sense - I'm learning about QFT as much as I can in
my spare time but this question may be "not even wrong".
Patrick Van Esch
Sep28-04, 10:19 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>\nArnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<4157E1B9.5030302@univie.ac.at>...\n\n> The standard theory gives an S-matrix (or rather an asymptotic series\n> for it) but not a dynamics at finite times. Clearly, measurements happen\n> in finite time, hence cannot be described at present in a fundamental way\n> (i.e., beyond the nonrelativistic QM approximation).\n\nIsn\'t this a too pessimistic view ? After all, the framework formally\nallows us to have the finite time evolution, it is just that it is\nplagued by infinities and inconsistencies (Haag ?). But as a "picture\nin the mind" cannot quantum fields be considered as having an evolving\nquantum state in Hilbert space (even if it screws up each time you\nwant to write it out explicitly) ?\n\ncheers,\npatrick.\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>Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<4157E1B9.5030302@univie.ac.at>...
> The standard theory gives an S-matrix (or rather an asymptotic series
> for it) but not a dynamics at finite times. Clearly, measurements happen
> in finite time, hence cannot be described at present in a fundamental way
> (i.e., beyond the nonrelativistic QM approximation).
Isn't this a too pessimistic view ? After all, the framework formally
allows us to have the finite time evolution, it is just that it is
plagued by infinities and inconsistencies (Haag ?). But as a "picture
in the mind" cannot quantum fields be considered as having an evolving
quantum state in Hilbert space (even if it screws up each time you
want to write it out explicitly) ?
cheers,
patrick.
Arnold Neumaier
Sep28-04, 10:20 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>\nBlake Winter wrote:\n>>The first article says:\n>>\'\'The nonabelian vector gauge fields are governed by a set of coupled,\n>>second order, nonlinear PDEs on Minkowski spacetime.\'\'\n>>Clearly, this mistakes the classical nonlinear dynamics of nonabelian\n>>gauge fields for nonlinear quantum dynamics. But relativistic QFT does\n>>not give a well-defined dynamics at all; all it defines is an S-matrix.\n>>So the article is void.\n>\n> I might add to my earlier questions, does this mean that in QFT we\n> can\'t start with some Psi describing the state of our fields at t = 0\n> and evolve it forward in time via d/dt Psi = H Psi, or some other such\n> equation?\n\nYes, indeed. There is no well-defined Hilbert space from which Psi could\nbe chosen. The H from canonical quantization acts on a free Fock space but\nattempts to turn this into something workable along the lines of\nordinary QM have failed.\n\nArnold Neumaier\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>Blake Winter wrote:
>>The first article says:
>>''The nonabelian vector gauge fields are governed by a set of coupled,
>>second order, nonlinear PDEs on Minkowski spacetime.''
>>Clearly, this mistakes the classical nonlinear dynamics of nonabelian
>>gauge fields for nonlinear quantum dynamics. But relativistic QFT does
>>not give a well-defined dynamics at all; all it defines is an S-matrix.
>>So the article is void.
>
> I might add to my earlier questions, does this mean that in QFT we
> can't start with some \Psi describing the state of our fields at t =
> and evolve it forward in time via d/dt \Psi = H \Psi, or some other such
> equation?
Yes, indeed. There is no well-defined Hilbert space from which \Psi could
be chosen. The H from canonical quantization acts on a free Fock space but
attempts to turn this into something workable along the lines of
ordinary QM have failed.
Arnold Neumaier
Arnold Neumaier
Sep28-04, 11:50 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>Blake Winter wrote:\n> But don\'t we see LQG attempting to evolve from one spin foam as a\n> starting point to another?\n\nI don\'t know about hypothetical theories like LQG.\nI was talking about the verifiable and verified consequences of\nrelativistic QFT, as revealed by calculations for QED, QCD, and the\nstandard model.\n\n\n> And can\'t we use path integrals to evolve\n> from one field configuration to another?\n\nThe problem with path integrals is that they are formal objects without\na clear meaning; whatever one tries to compute with them turns out to be\ninfinite. Only selected objects derived from path integrals can be given\nmeaning by means of the renormalization procedure. The books show how to\ngive meaning to S-matrix elements between asymptotic in and out states.\n\nBut I haven\'t seen a single article that gives meaning (i.e., finite,\nrenormalization scheme independent results) to, say, QED states at\nfinite t and their propagation in time.\n\n\n> Then by starting with some\n> Psi over the initial configurations we will be able to evolve it in\n> time, right? I guess I\'m wondering why its not true that the dynamics\n> are properly defined.\n\nPeople don\'t even know what an initial configuration Psi should be\n(i.e., from which space to take the states at finite t) in a\nrelativistic QFT; so how can they know how to propagate it...\n\n\nArnold Neumaier\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>Blake Winter wrote:
> But don't we see LQG attempting to evolve from one spin foam as a
> starting point to another?
I don't know about hypothetical theories like LQG.
I was talking about the verifiable and verified consequences of
relativistic QFT, as revealed by calculations for QED, QCD, and the
standard model.
> And can't we use path integrals to evolve
> from one field configuration to another?
The problem with path integrals is that they are formal objects without
a clear meaning; whatever one tries to compute with them turns out to be
infinite. Only selected objects derived from path integrals can be given
meaning by means of the renormalization procedure. The books show how to
give meaning to S-matrix elements between asymptotic in and out states.
But I haven't seen a single article that gives meaning (i.e., finite,
renormalization scheme independent results) to, say, QED states at
finite t and their propagation in time.
> Then by starting with some
> \Psi over the initial configurations we will be able to evolve it in
> time, right? I guess I'm wondering why its not true that the dynamics
> are properly defined.
People don't even know what an initial configuration \Psi should be
(i.e., from which space to take the states at finite t) in a
relativistic QFT; so how can they know how to propagate it...
Arnold Neumaier
Arnold Neumaier
Oct26-04, 12:55 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>Patrick Van Esch wrote:\n> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<4157E1B9.5030302@univie.ac.at>...\n>\n>>The standard theory gives an S-matrix (or rather an asymptotic series\n>>for it) but not a dynamics at finite times. Clearly, measurements happen\n>>in finite time, hence cannot be described at present in a fundamental way\n>>(i.e., beyond the nonrelativistic QM approximation).\n>\n> Isn\'t this a too pessimistic view ? After all, the framework formally\n> allows us to have the finite time evolution, it is just that it is\n> plagued by infinities and inconsistencies (Haag ?).\n\nYes. There is no consistent interaction picture in the sense we have it\nin QM. Nobody found a consistent notion in QFT of a state at finite times.\nWithout such a notion there cannot be a dynamical law.\n(However, one can compute - nonrigorously, in perturbation theory -\nsome time-dependent things, namely via the Schwinger-Keldysh\nformalism; see, e.g., http://theory.gsi.de/~vanhees/publ/green.pdf )\n\n\n> But as a "picture\n> in the mind" cannot quantum fields be considered as having an evolving\n> quantum state in Hilbert space (even if it screws up each time you\n> want to write it out explicitly) ?\n\nAs pictures in the mind one can have anything one finds helpful.\nProbably people working in QFT imagine something like a state evolution\nin Hilbert space underlying their formalism. After all, this is how\none justifies that the functional integral works.\n\nThe difficulties begin when one tries to draw conclusions that\nhave quantitative experimental consequences. This is a very efficient\ntest for distinguishing powerful intuition from feeble ghosts in one\'s\nmind.\n\nThis does not mean that there is no dynamical reality underlying\nrelativistic QFT. It only means that no one has been able to find\na working framework for it.\n\n\nArnold Neumaier\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>Patrick Van Esch wrote:
> Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<4157E1B9.5030302@univie.ac.at>...
>
>>The standard theory gives an S-matrix (or rather an asymptotic series
>>for it) but not a dynamics at finite times. Clearly, measurements happen
>>in finite time, hence cannot be described at present in a fundamental way
>>(i.e., beyond the nonrelativistic QM approximation).
>
> Isn't this a too pessimistic view ? After all, the framework formally
> allows us to have the finite time evolution, it is just that it is
> plagued by infinities and inconsistencies (Haag ?).
Yes. There is no consistent interaction picture in the sense we have it
in QM. Nobody found a consistent notion in QFT of a state at finite times.
Without such a notion there cannot be a dynamical law.
(However, one can compute - nonrigorously, in perturbation theory -
some time-dependent things, namely via the Schwinger-Keldysh
formalism; see, e.g., http://theory.gsi.de/~vanhees/publ/green.pdf )
> But as a "picture
> in the mind" cannot quantum fields be considered as having an evolving
> quantum state in Hilbert space (even if it screws up each time you
> want to write it out explicitly) ?
As pictures in the mind one can have anything one finds helpful.
Probably people working in QFT imagine something like a state evolution
in Hilbert space underlying their formalism. After all, this is how
one justifies that the functional integral works.
The difficulties begin when one tries to draw conclusions that
have quantitative experimental consequences. This is a very efficient
test for distinguishing powerful intuition from feeble ghosts in one's
mind.
This does not mean that there is no dynamical reality underlying
relativistic QFT. It only means that no one has been able to find
a working framework for it.
Arnold Neumaier
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