Tagged Questions

A gauge theory has internal degrees of freedom that do not affect the foretold physical outcomes of the theory. The theory has a Lie group of *continuous symmetries* of these internal degrees of freedom, *i.e.* the predicted physics under any transformation in this group on the degrees of freedom. ...

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7
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1answer
420 views

Why is color conserved in QCD?

According to Noether's theorem, global invariance under $SU(N)$ leads to $N^2-1$ conserved charges. But in QCD gluons are not conserved; color is. There are N colors, not $N^2-1$ colors. Am I ...
2
votes
0answers
223 views

Weak isospin and types of weak charge

My understanding is that QCD has three color charges that are conserved as a result of global SU(3) invariance. What about SU(2) weak? Does it have two types of charges? What I'm getting at is: U(1) ...
12
votes
2answers
550 views

Gauge invariance and diffeomorphism invariance in Chern-Simons theory

I have studied Chern-Simons (CS) theory somewhat and I am puzzled by the question of how diff. and gauge invariance in CS theory are related, e.g. in $SU(2)$ CS theory. In particular, I would like to ...
5
votes
2answers
265 views

Bianchi identity of a non-Abelian gauge theory?

How can one prove the Bianchi identity of a non-Abelian gauge theory? i.e. $$ \epsilon_{\mu \nu \lambda \sigma}(D_{\nu}F_{\lambda \sigma})^a=0 $$
9
votes
3answers
374 views

Chern-Simons degrees of freedom

I'm currently reading the paper http://arxiv.org/abs/hep-th/9405171 by Banados. I am just getting acquainted with the details of Chern-Simons theory, and I'm hoping that someone can explain/elaborate ...
5
votes
0answers
67 views

axial and vector resonances in composite higgs models

Is there a reason to believe that the axial resonances be heavier than the vector resonances in the composite higgs models? For instance, in http://arxiv.org/abs/0808.2071, to have zero tree level ...
1
vote
1answer
204 views

Interaction potential analysis from $\phi^4$ model

In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by $$S=\int d^d\! x ...
5
votes
0answers
86 views

sigma model on $S^1 \times S^3$

In arXiv:1207.3497 - 4D partition function on $S^1 \times S^3$ and 2D Yang-Mills with nonzero area, Yuji Tachikawa explains the partition function for an 4d $\mathcal{N}=2$ sigma model on $S^3 \times ...
3
votes
1answer
281 views

The theory of strings stretching between intersecting D-branes

I am trying to understand various aspects of intersecting D-branes in terms of the gauge theories on the worldvolume of the D-branes. One thing I'd like to understand is the worldvolume action for ...
7
votes
0answers
136 views

How to perform contour integral in Nekrasov's formula

My question is technical. It is about instanton counting calculation (see this paper). The partition function of SU(N) gauge theory with $N_f$ fundamental multiplets in k instanton background is ...
9
votes
1answer
414 views

What is the meaning of non-compactness in the context of $U(1)$ in gauge theories?

In John Preskill's review of monopoles he states Nowadays, we have another way of understanding why electric charge is quantized. Charge is quantized if the electromagnetic U(l)em gauge group ...
8
votes
3answers
587 views

Why is the Yang-Mills gauge group assumed compact and semi-simple?

What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories? I'd think that these hypotheses lead to physically ...
16
votes
2answers
397 views

Coulomb gauge fixing and “normalizability”

The Setup Let Greek indices be summed over $0,1,\dots, d$ and Latin indices over $1,2,\dots, d$. Consider a vector potential $A_\mu$ on $\mathbb R^{d,1}$ defined to gauge transform as $$ A_\mu\to ...
1
vote
0answers
58 views

Do Boundary Conditions depend on spin connections for gauge fields?

In the article arXiv:1206.5642, which talks about gauge fields in conical spacetime, I came across the statement in footnote 4 that the boundary conditions on the gauge field depend on the spin ...
5
votes
0answers
129 views

Master Field Large N limit

I would like to ask a question about the so-called ''Master Field''. As far as I understand, this represents a classical configuration in the large n limit (saddle point solution) but there is no ...
2
votes
1answer
179 views

Construction of the supersymmetric Faraday tensor

When I first learned gauge theories in my introductory quantum field theory course, I was taught that the Faraday (field-strength) tensor can be constructed by computing the commutator of the ...
8
votes
2answers
421 views

Geometrical significance of gauge invariance of the QED Lagrangian

The QED Lagrangian is invariant under $\psi(x) \to e^{i\alpha(x)} \psi (x)$, $A_{\mu} \to A_{\mu}- \frac{1}{e}\partial_{\mu}\alpha(x)$. What is the geometric significance of this result? Also why is ...
0
votes
0answers
45 views

Good Books on Gauge Theory [duplicate]

Possible Duplicate: Comprehensive book on group theory for physicists? I'm having a hard time trying to get my head around the fundamentals of gauge theory. I've taken classes in QFT and ...
3
votes
1answer
736 views

Local and Global Symmetries

Could somebody point me in the direction of a mathematically rigorous definition local symmetries and global symmetries for a given (classical) field theory? Heuristically I know that global ...
5
votes
2answers
2k views

What is the difference between a photon and a phonon?

More specifically, how does a wave-particle duality differ from a quasiparticle/collective excitation? What makes a photon a gauge boson and a phonon a Nambu–Goldstone boson?
8
votes
1answer
673 views

Diffeomorphisms, Isometries And General Relativity

Apologies if this question is too naive, but it strikes at the heart of something that's been bothering me for a while. Under a diffeomorphism $\phi$ we can push forward an arbitrary tensor field $F$ ...
8
votes
1answer
358 views

Introduction to Gauge Symmetries: Good, Bad or Ugly?

I'm trying to come up with a good (as in intuitive and not 'too wrong') definition of a gauge symmetry. This is what I have right now: A dynamical symmetry is a (differentiable) group of ...
2
votes
2answers
265 views

Is the artificial gauge field a gauge field?

The so-called artificial gauge fields are actually the Berry connection. They could be $U(1)$ or $SU(N)$ which depends on the level degeneracy. For simplicity, let's focus on $U(1)$ artificial gauge ...
12
votes
1answer
304 views

How can two time theories be compactified to 3+1 without any Kaluza-Klein remnants

I have recently been looking into the two-time theories and the implied concepts. For me this seems slightly hard to grasp. How can I see the basic concept in this theory in a fundamental way based ...
13
votes
4answers
977 views

To which extent is general relativity a gauge theory?

In quantum mechanics, we know that a change of frame -- a gauge transform -- leaves the probability of an outcome measurement invariant (well, the square modulus of the wave-function, i.e. the ...
3
votes
0answers
49 views

Attractiveness of spin 2 gauge theories [duplicate]

Possible Duplicate: Why is gravitation force always attractive? I have heard that the attractiveness of gravitation is due to the fact that it is a spin 2 gauge theory. Why is this so? I ...
1
vote
1answer
218 views

observable quantities are gauge invariant?

I have a simply question, that is whether spatial velocity is gauge invariant. It is seems that under a infinitesimal coordinate transformation the velocity is just transform as other vectors, and it ...
3
votes
1answer
333 views

About the gauge invariance of Chern-Simons' theory (in local coordinates)

I am aware of the differential form language proof of the fact that for arbitrary gauge transformations the Chern-Simons' term shifts by a WZW term (on the boundary). But I am getting confused if ...
6
votes
0answers
144 views

Gauge-invariance of pole mass using Ward Identity

I am able to explicitly verify to one-loop order that pole masses are independent of the choice of gauge paramter. But how do I use the Ward-Identity/Taylor-Slavnov identity show that the position of ...
1
vote
1answer
172 views

In a gauge theory, are two states related by a global phase transformation identified?

In a gauge theory (non-abelian for this question), I am told that two states $|\psi\rangle$ and $|\phi\rangle$ are to be identified if they are related by a gauge transformation $U(x)$ ...
5
votes
1answer
192 views

Yang Mills Hamiltonian: why do we use the Weyl's temporal gauge?

Do you know why in the quantization of SU(2) Yang Mills Gauge Theory, it is always chosen the Weyl (temporal) gauge to derive the Hamiltonian? Is it possible to fix another gauge?
6
votes
1answer
561 views

Faddeev-Popov ghost propagator in canonical quantization

Obtaining the propagator for the Faddeev-Popov (FP) ghosts from the path integral language is straightforward. It is simply $$\langle T(c(x) \bar c(y))\rangle~=~\int\frac{d^4 p}{(2\pi)^4}\frac{i ...
1
vote
4answers
193 views

Cubic term in gauge theories

In ordinary classical gauge theories the term $-\frac{1}{2}\mathrm{Tr}(F_{\mu\nu}F^{\mu\nu})=-\frac{1}{4}F^a_{\mu\nu}F_a^{\mu\nu}$ in the Lagrangian is completely natural. A somehow rare term would be ...
8
votes
1answer
259 views

7 sphere, is there any physical interpretation of exotic spheres?

Basically an exotic sphere is topologically a sphere, but doesn't look like a one. Or more accurately: homeomorphic but not diffeomorphic to the standard Euclidean n-sphere The first exotic ...
2
votes
0answers
39 views

What is the physical meaning of the higher order structure functions in the BRST quantization of open algebras?

What is the physical meaning of the higher order structure functions in the BRST quantization of open algebras? As opposed to formal algebraic manipulations. Thanks.
2
votes
2answers
296 views

Path integral on matrix model

I was looking at a 0-dimensional matrix model, where the variables are $N\cdot N$ Hermitean matrices. It had a gauge symmetry, e.g. $U(N)$. And in the path integral, the Faddeev-Popov trick was used. ...
3
votes
1answer
466 views

Large gauge transformations

I would like to understand what is the importance of large gauge transformations. I read that these gauge transformation cannot be deformed to the identity, but why should we care about that?
5
votes
2answers
458 views

Gauge fixing and equations of motion

Consider an action that is gauge invariant. Do we obtain the same information from the following: Find the equations of motion, and then fix the gauge? Fix the gauge in the action, and then find the ...
4
votes
1answer
166 views

Weak isospin confinement?

According to the Wikipedia article on color confinement: The current theory is that confinement is due to the force-carrying gluons having color charge [...], i.e. because the gauge group is ...
1
vote
1answer
70 views

How is $ g^2 N$ held fixed in the large N limit?

In 't Hooft's original paper: http://igitur-archive.library.uu.nl/phys/2005-0622-152933/14055.pdf he takes $N \rightarrow \infty $ while $ g^2 N$ is held fixed. Is this just a toy model? Or is there ...
2
votes
3answers
181 views

Quantizing first-class constraints for open algebras: can Hermiticity and noncommutativity coexist?

An open algebra for a collection of first-class constraints, $G_a$, $a=1,\cdots, r$, is given by the Poisson bracket $\{ G_a, G_b \} = {f_{ab}}^c[\phi] G_c$ classically, where the structure constants ...
3
votes
1answer
532 views

Gauss law in classical U(1) gauge theory

I can see that $a_{0}$ is not an independent field and Gauss law is a constraint on the theory arising from field equations. But, I don't get the geometrical picture. Let $A$ be the space of all ...
3
votes
0answers
202 views

Pseudo scalar mass and Pure scalar mass

Since the only difference between pseudo scalar and a scalar term is just a change of sign under a parity inversion, is it possible that both of them be present in the same field and interact? For ...
6
votes
2answers
564 views

Intuition for gauge parallel transport (Wilson loops)

I'm looking for a geometrical interpretation of the statement that "Wilson loop is a gauge parallel transport". I have seen QFT notes describe U(x,y) as "transporting the gauge transformation", and ...
3
votes
1answer
209 views

For nonabelian Yang-Mills in the Coulomb phase, can soft gluons render the charge orientation of charged particles indefinite?

For nonabelian Yang-Mills in the Coulomb phase, can soft gluons render the charge orientation of charged particles indefinite? Let's say the gauge group is a nonabelian simple Lie group G. Suppose ...
3
votes
2answers
139 views

What exactly is the weak portion of the SM gauge group?

This Wikipedia article: http://en.wikipedia.org/wiki/Left%E2%80%93right_symmetry states that the weak part of the SM gauge group is not $SU(2)_L \times U(1)_Y$ but $ \frac{ SU(2)_L \times ...
4
votes
2answers
609 views

Counting degrees of freedom in presence of constraints

In a $N$ dimensional phase space if I have $M$ 1st class and $S$ 2nd class constraints, then I have $N-2M-S$ degrees of freedom in phase space. How can I calculate the degrees of freedom in ...
3
votes
4answers
782 views

First class and second class constraints

Hello I am working on a project that involves the constraints. I checkout the paper of Dirac about the constraints as well as some other resources. But still confuse about the first class and second ...
3
votes
1answer
242 views

Does spontanous symmetry breaking affect Noethers theorem?

Does spontanous symmetry breaking affect the existence of a conserved charge? And how does depend on whether we look at a classical or a quantum field theory (e.g. the weak interacting theory)? ...
3
votes
0answers
126 views

Derivation of the enhancement of U(1)$_L$ x U(1)$_R$ to SU(2)$_L$ x SU(2)$_R$ at the self-dual radius

Towards the end of the paragraph with the title String theory's added value 2: enhanced non-Abelian symmetries at self-dual radii and abstract C with current algebras of this article, it is explained ...