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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92 views

Is there a critical order of the Abelian gauge theory in (2+1)D

In (2+1)D spacetime, it is known that the $U(1)$ gauge theory is always confined (according to Polyakov), while the $\mathbb{Z}_2$ gauge theory can support a deconfined phase. Now consider a generic ...
3
votes
0answers
49 views

Holomorphic coupling as a source for gaugino condensation

On the top of page 23 of hep-th/03061119, it is pointed out that treating the holomorphic gauge coupling $\tau$ as a background (spurion) superfield allows one to think of its $F$-term, $F_\tau$ as ...
13
votes
4answers
765 views

Can we measure an electromagnetic field?

As far as I can check, the Aharonov-Bohm effect is not -- contrary to what is claimed in the historical paper -- a demonstration that the vector potential $A$ has an intrinsic existence in quantum ...
4
votes
0answers
124 views

What is the fundamental difference between ghost and auxiliary fields?

I am somehow confused by the notion of auxiliary fields, such as for example the fields $F$ and $D$ which appear in supersymmetry, and the notion of ghost fields which appear for example in the BRST ...
3
votes
2answers
361 views

primary constraints for constrained Hamiltonian systems

I would be most thankful if you could help me clarify the setting of primary constraints for constrained Hamiltonian systems. I am reading "Classical and quantum dynamics of constrained Hamiltonian ...
3
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0answers
68 views

Does the ensemble of effective Lagrangians in the String theory landscape mostly include gauge theories?

String theory false vacua can be described by effective Lagrangians at low energy. Is there generally a correspondence between these effective Lagrangians and SU(N) gauge theories? Or do the effective ...
7
votes
1answer
118 views

Do instantons support quantum bound states?

When one quantizes a scalar in the 1+1 dimensions in the kink background of a double well potential, one finds a spectrum that includes: (1) a zero mode corresponding to the classical particle ...
1
vote
1answer
313 views

Are string theories gauge theories?

The wikipedia page for String Theory lists SO(32) and E8×E8 as group symmetries of some of the string theory types, and the page on E8 says: E8×E8 is the gauge group of one of the two types of ...
1
vote
1answer
189 views

Phase shift in electromagnetic potential

In Aharonov-Bohm effect, how to derive that the wave function of a electric charge $q$ acquires a phase shift $\phi=\frac{q}{\hbar}\int \mathbf{A} \cdot d\mathbf{x}$ after travelling in the non-zero ...
7
votes
1answer
821 views

How can a massless boson (Gluon) mediate the short range Strong Force?

I thought massless particles were mediators for long range forces such as electromagnetism and gravitation. How can the massless gluon mediate the short range strong force?
5
votes
0answers
71 views

The consistency conditions of constrained Hamiltonian systems

I am studying the Hamiltonian description of a constrained system. There are some questions puzzled me for days, which I have been stuck on it. From the lagrangian, we can obtain the primary ...
2
votes
1answer
180 views

Moose Models (Purpose, Examples)

A problem set for my QFT class is titled "Moose Models" and deals with the moose model for a gauge symmetry of $U(1)\times U(1)$. I was wondering if I could get an explanation of what a Moose Model ...
7
votes
1answer
428 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
225 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
560 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
290 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
376 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
209 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
286 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
137 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 ...
11
votes
1answer
447 views

What is (meant by) a non-compact $U(1)$ Lie group?

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 ...
3
votes
2answers
161 views

Proof of quantization of magnetic charge of monopoles using homotopy groups

Suppose we place a monopole at the origin $\{{\bf 0}\}$, and the gauge field is well-definded in region $\mathbb R^3-\{0\}$ which is homomorphic to a sphere $S^2$. Then the total manifold is $U(1)$ ...
8
votes
3answers
607 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
400 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 ...
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0answers
59 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
132 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
183 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
429 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
770 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
695 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
374 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
269 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
305 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
1k 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
223 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
339 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
176 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
196 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
567 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
196 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
268 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
302 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
481 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?