Re: Stupid questions [Archive]

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Thomas Dent

Jul2-04, 06:09 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\nCreighton Hogg <wchogg@hep.wisc.edu> wrote\n\n> Are there other valid frameworks for describing forces, at energy levels\n> ~10TeV or lower, besides gauge interactions (I\'m including string theory\n> here because at low energy the contact interactions of strings have to\n> look like gauge interactions)? I seem to remember being\n> told in a QFT class that you\'re not allowed to have any other kinds of\n> interactions, but I honestly don\'t understand why. I\'m just wondering if\n> there\'s other options or if, at sufficiently low energy, everything *must*\n> look a QFT with gauge interactions.\n\n\nWhy don\'t you ask one of the many particle theory professors at\nWisconsin? They don\'t bite. (At least, not all of them.)\n\nIt\'s certainly not true that you are *only* allowed gauge\ninteractions. Perhaps you are misremembering the QFT class. If you\nhave only fermions and vectors and restrict yourself to renormalizable\ntheories, then this is the case. (That is, if you don\'t count fermion\nmass terms as \'interactions\'.)\n\nHowever you can have four-fermion (or 2n-fermion) interactions which\nare not due to exchange of gauge bosons - they just turn out to be\nnonrenormalizable in general. As Weinberg pointed out (1979), this is\nnot an automatic disaster. Nonrenormalizable theories can give useful\nresults if the cutoff is sufficiently high. For example the Fermi\ntheory works perfectly well at nuclear physics energies. And, of\ncourse, gravity is nonrenormalizable.\n\nIf you allow scalar particles, the number of non-gauge interactions\nincreases markedly. At renormalizable level you have phi^3 and phi^4\noperators and in general you can have phi^n and even operators with\nderivatives (e.g. (d phi)^2 phi^2). Also Yukawa interactions (two\nfermions and one scalar) which are renormalizable.\n\nYou can write down a perfectly good quantum field theory without any\ngauge symmetry at all and without it being renormalizable and still\nmake some predictions. This is what chiral perturbation theory (Gasser\n& Leutwyler 1984-1985) does, for example.\n\nIt is a different question as to what the *underlying* or\n*fundamental* theory is. Since gravity exists, the underlying theory\ncannot be just Yang-Mills. String models do tend to produce Yang-Mills\nas a 4d low energy limit, but they also have a large scalar sector\nwhich may include stuff which isn\'t constrained by 4d gauge symmetry.\n\nAny further questions?\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>Creighton Hogg <wchogg@hep.wisc.edu> wrote

> Are there other valid frameworks for describing forces, at energy levels
> ~10TeV or lower, besides gauge interactions (I'm including string theory
> here because at low energy the contact interactions of strings have to
> look like gauge interactions)? I seem to remember being
> told in a QFT class that you're not allowed to have any other kinds of
> interactions, but I honestly don't understand why. I'm just wondering if
> there's other options or if, at sufficiently low energy, everything *must*
> look a QFT with gauge interactions.

Why don't you ask one of the many particle theory professors at
Wisconsin? They don't bite. (At least, not all of them.)

It's certainly not true that you are *only* allowed gauge
interactions. Perhaps you are misremembering the QFT class. If you
have only fermions and vectors and restrict yourself to renormalizable
theories, then this is the case. (That is, if you don't count fermion
mass terms as 'interactions'.)

However you can have four-fermion (or 2n-fermion) interactions which
are not due to exchange of gauge bosons - they just turn out to be
nonrenormalizable in general. As Weinberg pointed out (1979), this is
not an automatic disaster. Nonrenormalizable theories can give useful
results if the cutoff is sufficiently high. For example the Fermi
theory works perfectly well at nuclear physics energies. And, of
course, gravity is nonrenormalizable.

If you allow scalar particles, the number of non-gauge interactions
increases markedly. At renormalizable level you have \phi^3 and \phi^4
operators and in general you can have \phi^n and even operators with
derivatives (e.g. (d \phi)^2 \phi^2). Also Yukawa interactions (two
fermions and one scalar) which are renormalizable.

You can write down a perfectly good quantum field theory without any
gauge symmetry at all and without it being renormalizable and still
make some predictions. This is what chiral perturbation theory (Gasser
& Leutwyler 1984-1985) does, for example.

It is a different question as to what the *underlying* or
*fundamental* theory is. Since gravity exists, the underlying theory
cannot be just Yang-Mills. String models do tend to produce Yang-Mills
as a 4d low energy limit, but they also have a large scalar sector
which may include stuff which isn't constrained by 4d gauge symmetry.

Any further questions?

Creighton Hogg

Jul2-04, 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>On 2 Jul 2004, Thomas Dent wrote:\n\n>\n>\n> Creighton Hogg <wchogg@hep.wisc.edu> wrote\n>\n> > Are there other valid frameworks for describing forces, at energy levels\n> > ~10TeV or lower, besides gauge interactions (I\'m including string theory\n> > here because at low energy the contact interactions of strings have to\n> > look like gauge interactions)? I seem to remember being\n> > told in a QFT class that you\'re not allowed to have any other kinds of\n> > interactions, but I honestly don\'t understand why. I\'m just wondering if\n> > there\'s other options or if, at sufficiently low energy, everything *must*\n> > look a QFT with gauge interactions.\n>\n>\n> Why don\'t you ask one of the many particle theory professors at\n> Wisconsin? They don\'t bite. (At least, not all of them.)\n\nYeah, I like all of the people I\'ve met from the 5th floor. It\'s not\nreally a question for work, just my own idle musings, so I\'d feel pretty\nrude bugging them.\n\n> It\'s certainly not true that you are *only* allowed gauge\n> interactions. Perhaps you are misremembering the QFT class. If you\n> have only fermions and vectors and restrict yourself to renormalizable\n> theories, then this is the case. (That is, if you don\'t count fermion\n> mass terms as \'interactions\'.)\n>\n> However you can have four-fermion (or 2n-fermion) interactions which\n> are not due to exchange of gauge bosons - they just turn out to be\n> nonrenormalizable in general. As Weinberg pointed out (1979), this is\n> not an automatic disaster. Nonrenormalizable theories can give useful\n> results if the cutoff is sufficiently high. For example the Fermi\n> theory works perfectly well at nuclear physics energies. And, of\n> course, gravity is nonrenormalizable.\n>\n> If you allow scalar particles, the number of non-gauge interactions\n> increases markedly. At renormalizable level you have phi^3 and phi^4\n> operators and in general you can have phi^n and even operators with\n> derivatives (e.g. (d phi)^2 phi^2). Also Yukawa interactions (two\n> fermions and one scalar) which are renormalizable.\n>\n> You can write down a perfectly good quantum field theory without any\n> gauge symmetry at all and without it being renormalizable and still\n> make some predictions. This is what chiral perturbation theory (Gasser\n> & Leutwyler 1984-1985) does, for example.\n>\n> It is a different question as to what the *underlying* or\n> *fundamental* theory is. Since gravity exists, the underlying theory\n> cannot be just Yang-Mills. String models do tend to produce Yang-Mills\n> as a 4d low energy limit, but they also have a large scalar sector\n> which may include stuff which isn\'t constrained by 4d gauge symmetry.\n>\n> Any further questions?\n>\n\nYou definately gave me some food for thought, thanks. I realize what I\nwas mostly wondering is if there were valid models of vector boson\nexchange that don\'t have a guage symmetry. I\'m not worried so much by\nwhether or not the interaction is renormalizable. Like I said, this is\npretty much just idle musing on my part: curiosity as to how much freedom\nin phenomenologic models to fit the data that will come out of LHC we have\nother than the same ol\' theories defined almost entirely but what gauge\ngroup you choose.\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 2 Jul 2004, Thomas Dent wrote:

>
>
> Creighton Hogg <wchogg@hep.wisc.edu> wrote
>
> > Are there other valid frameworks for describing forces, at energy levels
> > ~10TeV or lower, besides gauge interactions (I'm including string theory
> > here because at low energy the contact interactions of strings have to
> > look like gauge interactions)? I seem to remember being
> > told in a QFT class that you're not allowed to have any other kinds of
> > interactions, but I honestly don't understand why. I'm just wondering if
> > there's other options or if, at sufficiently low energy, everything *must*
> > look a QFT with gauge interactions.
>
>
> Why don't you ask one of the many particle theory professors at
> Wisconsin? They don't bite. (At least, not all of them.)

Yeah, I like all of the people I've met from the 5th floor. It's not
really a question for work, just my own idle musings, so I'd feel pretty
rude bugging them.

> It's certainly not true that you are *only* allowed gauge
> interactions. Perhaps you are misremembering the QFT class. If you
> have only fermions and vectors and restrict yourself to renormalizable
> theories, then this is the case. (That is, if you don't count fermion
> mass terms as 'interactions'.)
>
> However you can have four-fermion (or 2n-fermion) interactions which
> are not due to exchange of gauge bosons - they just turn out to be
> nonrenormalizable in general. As Weinberg pointed out (1979), this is
> not an automatic disaster. Nonrenormalizable theories can give useful
> results if the cutoff is sufficiently high. For example the Fermi
> theory works perfectly well at nuclear physics energies. And, of
> course, gravity is nonrenormalizable.
>
> If you allow scalar particles, the number of non-gauge interactions
> increases markedly. At renormalizable level you have \phi^3 and \phi^4
> operators and in general you can have \phi^n and even operators with
> derivatives (e.g. (d \phi)^2 \phi^2). Also Yukawa interactions (two
> fermions and one scalar) which are renormalizable.
>
> You can write down a perfectly good quantum field theory without any
> gauge symmetry at all and without it being renormalizable and still
> make some predictions. This is what chiral perturbation theory (Gasser
> & Leutwyler 1984-1985) does, for example.
>
> It is a different question as to what the *underlying* or
> *fundamental* theory is. Since gravity exists, the underlying theory
> cannot be just Yang-Mills. String models do tend to produce Yang-Mills
> as a 4d low energy limit, but they also have a large scalar sector
> which may include stuff which isn't constrained by 4d gauge symmetry.
>
> Any further questions?
>

You definately gave me some food for thought, thanks. I realize what I
was mostly wondering is if there were valid models of vector boson
exchange that don't have a guage symmetry. I'm not worried so much by
whether or not the interaction is renormalizable. Like I said, this is
pretty much just idle musing on my part: curiosity as to how much freedom
in phenomenologic models to fit the data that will come out of LHC we have
other than the same ol' theories defined almost entirely but what gauge
group you choose.

Thomas Dent

Jul4-04, 07:39 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>\nCreighton Hogg <wchogg@hep.wisc.edu> wrote\n\n> > Why don\'t you ask one of the many particle theory professors at\n> > Wisconsin? They don\'t bite. (At least, not all of them.)\n>\n> Yeah, I like all of the people I\'ve met from the 5th floor. It\'s not\n> really a question for work, just my own idle musings, so I\'d feel pretty\n> rude bugging them.\n\nWell, if you can put together an informed, concise question, it won\'t\nconstitute bugging.\n\n> > It\'s certainly not true that you are *only* allowed gauge\n> > interactions. Perhaps you are misremembering the QFT class. If you\n> > have only fermions and vectors and restrict yourself to renormalizable\n> > theories, then this is the case. (That is, if you don\'t count fermion\n> > mass terms as \'interactions\'.)\n\n(...)\n\n> I realize what I was mostly wondering is if there were valid models of\n> vector boson exchange that don\'t have a gauge symmetry. I\'m not worried\n> so much by whether or not the interaction is renormalizable. Like I said,\n> this is pretty much just idle musing on my part: curiosity as to how much\n> freedom in phenomenologic models to fit the data that will come out of LHC\n> we have other than the same ol\' theories defined almost entirely but what\n> gauge group you choose.\n\nSo, if you are interested specifically in theories of vectors, that\nnarrows it down quite a lot. There is a theorem somewhere saying that\nif you require certain properties such as unitarity, renormalizability\netc. the only consistent theory (in Minkowski space) with vectors is\nYang-Mills. Unfortunately I can\'t remember the exact conditions to\nprove the theorem. No doubt some prof. would know.\n\nThe fact that rho mesons, for example, exist, shows that vectors need\nnot be gauge bosons. Nuclear theory sometimes involves a sort of\nphenomenological model of nucleon-nucleon forces involving (scalar\nand) vector exchange which isn\'t gauge theory. But it\'s not a very\nnice model because the cutoff is very low above which you lose\nunitarity...\n\nIf you are thinking of the W and Z, there is of course the LEP\nprecision data that places very severe limits on what they can be.\n>From this they look pretty darn identical to gauge bosons.\nCompositeness is ruled out up to quite high scales for example.\n\nIncidentally you will find sci.physics.research a lot more convenient\nfor this sort of question than sci.physics.\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>Creighton Hogg <wchogg@hep.wisc.edu> wrote

> > Why don't you ask one of the many particle theory professors at
> > Wisconsin? They don't bite. (At least, not all of them.)
>
> Yeah, I like all of the people I've met from the 5th floor. It's not
> really a question for work, just my own idle musings, so I'd feel pretty
> rude bugging them.

Well, if you can put together an informed, concise question, it won't
constitute bugging.

> > It's certainly not true that you are *only* allowed gauge
> > interactions. Perhaps you are misremembering the QFT class. If you
> > have only fermions and vectors and restrict yourself to renormalizable
> > theories, then this is the case. (That is, if you don't count fermion
> > mass terms as 'interactions'.)

(...)

> I realize what I was mostly wondering is if there were valid models of
> vector boson exchange that don't have a gauge symmetry. I'm not worried
> so much by whether or not the interaction is renormalizable. Like I said,
> this is pretty much just idle musing on my part: curiosity as to how much
> freedom in phenomenologic models to fit the data that will come out of LHC
> we have other than the same ol' theories defined almost entirely but what
> gauge group you choose.

So, if you are interested specifically in theories of vectors, that
narrows it down quite a lot. There is a theorem somewhere saying that
if you require certain properties such as unitarity, renormalizability
etc. the only consistent theory (in Minkowski space) with vectors is
Yang-Mills. Unfortunately I can't remember the exact conditions to
prove the theorem. No doubt some prof. would know.

The fact that \rho mesons, for example, exist, shows that vectors need
not be gauge bosons. Nuclear theory sometimes involves a sort of
phenomenological model of nucleon-nucleon forces involving (scalar
and) vector exchange which isn't gauge theory. But it's not a very
nice model because the cutoff is very low above which you lose
unitarity...

If you are thinking of the W and Z, there is of course the LEP
precision data that places very severe limits on what they can be.
>From this they look pretty darn identical to gauge bosons.
Compositeness is ruled out up to quite high scales for example.

Incidentally you will find sci.physics.research a lot more convenient
for this sort of question than sci.physics.