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. ...

learn more… | top users | synonyms

3
votes
1answer
82 views

Anomaly, Ward identity [closed]

While studying notes on anomaly by Adel Bilal (http://arxiv.org/abs/0802.0634), I stuck in a calculation. Here it goes as follows: The three-current correlator in perturbation theory as a one-loop ...
8
votes
2answers
573 views

Why do we use gauges in Maxwell equation?

While solving the Maxwell's equation we often use the Lorenz or Coulomb gauge, but why is that? Are the equations unsolvable if the gauge is not fixed? Or is it just for the simplicity?
5
votes
0answers
79 views

Is there an algorithm to diagonalize a matrix using gauge transformations

I have two matrices $U(\lambda, x,t)$ and $V(\lambda, x,t)$, where $\lambda$ is a parameter, which belong to the $sl(2)$ algebra, and satisfy the zero-curvature equation $$ \partial_t U - \partial_x V ...
4
votes
1answer
84 views

Why is Seiberg duality called an electromagnetic duality?

An electromagnetic duality is a duality that maps electric to magnetic degrees of freedom of two distinct theories. Apart from source-less Maxwell electrodynamics, other theories require magnetic ...
3
votes
1answer
227 views

Large gauge transformations for higher p-form gauge fields

Question: What is the large gauge transformations for higher p-form gauge field on a spatial d-dimensional torus $T^d$ or a generic (compact) manifold $M$? for p=1,2,3, etc or any other integers. Is ...
3
votes
1answer
75 views

How many glueballs are there?

As I understand there are eight types of gluons (linear combinations of color/anticolor pairs with varying amplitudes) which can combine (for very short periods) to form glueballs. If there were no ...
4
votes
2answers
94 views

What S means in S-duality?

As I know, there are many dualities related to S-duality. For example, Montonen-Olive duality, Seiberg duality. and so on. so, I wonder that what "S" means in the term "S-duality". If this is a stupid ...
4
votes
1answer
48 views

What kind of fields can couple naturally to a $p$-form gauge fields in a Lagrangian?

Ordinary $U(1)$ gauge fields can naturally couple to classical fields such as spin-$1/2$ fields via the Dirac Lagrangian, or to complex spin-$0$ fields via the obvious covariant derivative coupling, ...
1
vote
1answer
57 views

Classical Yang Mills vacuum

What is the vacuum of classical Yang Mills theory $$\mathcal{L} = - \frac14 F^{a \mu \nu} F^a_{\mu \nu}~?$$ Is it simply $A^a_\mu=0$ for all its components?
0
votes
0answers
40 views

Equality of renormalized coupling constant

I want to show, that the renormalized coupling constants of a SU(N) Yang-Mills field with fermions included, are all equal. In the most textbooks it is written, that this could been shown by the Ward-...
0
votes
0answers
32 views

Symmetry breaking with adjoint matter, departing from vacuum in different way

$$L=-\frac{1}{4}TrF_{\mu\nu}F^{\mu\nu}+\frac{1}{2}D_\mu\phi D^\mu \phi -\lambda V(\phi)$$ Say we have a potential $V(\phi)=(|\phi|^2-v^2)^2$, and 3-component real scalar field $\phi=(\phi_1, \phi_2, \...
0
votes
1answer
62 views

Infinitesimal gauge invariance of Yang--Mills Lagrangian

Under an infinitesimal gauge transformation $g(x) = 1 - i\alpha{}_i(x)T{}^i$, where $[T{}^a, T{}^b] = if{}^{ab}{}_c T{}^c$, I want to know what happens to the Lagrangian $\mathcal{L} = F{}_{a\mu\nu}F{}...
1
vote
1answer
58 views

Magnetic monopoles gauge theories

I'm quoting 't Hooft: "[...] Locally stable field configurations may exist that have some topological twist in them [...].Careful analysis of the existing Lie groups and the way they may be ...
5
votes
1answer
70 views

Particle on $S^1$ and $U(1)$-principal bundle

I have a question arisen from a simple QM problem: let consider a boson on $S^1$ minimally coupled with a constant gauge field $A$. Taking the stationary Schrödinger (S) or Klein-Gordon (KG) equation ...
3
votes
2answers
205 views

How can Maxwell theory be viewed in terms of two-layer structure?

I'm trying to learn more about Maxwell equations and stumbled upon an essay by professor Freeman J. Dyson from Princeton. He explained Maxwell theory in a very interesting way. The modem view of ...
4
votes
1answer
280 views

Does the low-energy gauge structure depend on the choice of $SU(2)$ gauge freedom?

The starting point and notations used here are presented in Two puzzles on the Projective Symmetry Group(PSG)?. As we know, Invariant Gauge Group(IGG) is a normal subgroup of Projective Symmetry ...
1
vote
1answer
80 views

Unphysical degrees of freedom in the Yang Mills Lagrangian [duplicate]

Im taking my first course in QFT and has stumbled upon something that I do not understand. Given the Yang Mills lagrangian $$\mathcal{L} = -\frac{1}{4}F^{a}_{\mu \nu}F^{a\mu \nu}$$ with $F^{\mu \nu}...
1
vote
1answer
51 views

Left-right topology

Are there non-trivial topological solutions (in particular 't Hooft-Polyakov magnetic monopoles) associated with the (local) breaking \begin{equation} SU(2)_R \times SU(2)_L \times U(1)_{B-L} \to SU(...
3
votes
1answer
195 views

Showing closure of the SUSY algebra of a free abelian gauge multiplet

Given the complete supersymmetric lagrangian of a free abelian gauge multiplet $$ \mathcal{L} = -\frac{1}{4} F_{\mu\nu} F^{\mu\nu} + i \bar{\lambda} \bar{\sigma}^\mu \partial_\mu \lambda + \frac{1}{2} ...
0
votes
1answer
75 views

Is the standard model a quantized gauge theory?

I have studied some quantum field theory and gauge theory but I am definitely not an expert. I am aware that in quantizing electrodynamics one has to fix a gauge. I have read that for general gauge ...
0
votes
0answers
16 views

how to construct a model with fully broken SU(2) gauge symmetry, in which the masses of all three vector bosons are different

When we do the spontaneous symmetry breaking of SU(2) local gauge symmetry, the three vector fields acquire mass which is equal for all three of them. Now how do I construct a model in which the ...
2
votes
2answers
60 views

Do Weyl fermions carry electric charge?

Do Weyl fermions carry ordinary electric charge? That is, do they interact with, for instance, electrons or photons?
0
votes
0answers
33 views

Simplify $K$-matrix

2+1D Abelian topologically ordered states are believed to be described by multicomponent $U(1)$ Chern-Simons theories, with Lagrangian \begin{equation} \mathcal{L}=\frac{K_{IJ}}{4\pi}\epsilon^{\mu\nu\...
4
votes
3answers
106 views

Gauge invariance in classical electrodynamics

I think that I don't fully understand concept of gauge invariance. Suppose we have a Lagrangian for classical ED which is: $$\mathcal{L} = -\frac{1}{4} (F_{\mu \nu})^2 - j^{\mu}A_{\mu}.$$ First part ...
0
votes
1answer
58 views

Global Anomaly and Ward Identity

This question is a continuation of the answer posted for this question about anomalies. What happens to the Ward identity corresponding to a global symmetry if that symmetry is anomalous? I mean, is ...
1
vote
1answer
92 views

Global anomaly for discrete groups

We know that: a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformations that would otherwise be preserved in the ...
0
votes
0answers
48 views

Explicit derivative of Chern-Simons current

I know that for a Chern-Simons 3-form $\omega=\operatorname{Tr}\left[F\wedge A-\frac{1}{3}A\wedge A\wedge A\right]$, with $F=A\wedge A +\operatorname{d}A$, I should get $\operatorname{d}\omega=\...
1
vote
0answers
17 views

On the action of superconformal generators in maximally supersymmetric Yang-Mills

Consider maximally supersymmetric Yang-Mills theory in 3+1 dimensions. This theory has 32 supercharges: 16 ordinary ones, conventionally labeled $Q$; and 16 superconformal ones, conventionally ...
2
votes
0answers
29 views

Gauge mediated SUSY breaking

I have seen it claimed that in SUSY gauge mediated breaking there can be no flavour changing terms because the mediation is flavour blind. What does this mean and how does it work?
1
vote
1answer
59 views

Which groups can be lattice gauge groups?

Let me state first off that in this question I am most interested in lattice gauge theories, and not necessarily with Fermion couplings. But if Fermions and continuum gauge theories can also be ...
4
votes
1answer
85 views

What gauge field can be constructed from Lorentz symmetry?

You can take a global symmetry and promote it to a local gauge symmetry by introducing an appropriate gauge field and upgrading the partial derivative to a covariant derivative. The photon field ...
13
votes
0answers
304 views

How to apply the Faddeev-Popov method to a simple integral

Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
4
votes
1answer
435 views

$SU(2)$ Yang-Mills EOM

I'm having trouble with some indices on my yang-mills lagrangian. I have a gauge group $SU(2)$ and a field strength tensor $$ F_{ab}^{i}=\partial_{a}A^{i}_{b}-\partial_{b}A^{i}_{a}+\epsilon^{i}_{\,\,...
1
vote
0answers
57 views

Non-null hessian condition for regular dynamical systems

I'm "researching" on unquantised Yang-Mills theory. For that I'm studying the Dirac's method for singular constrained systems and having problems to follow the first considerations on that matter. I ...
3
votes
1answer
144 views

Observation of gauge in artificial magnetic fields

In the ultracold atom community, an "artificial gauge field" or "artificial magnetic field" is a spatially varying hopping phase somehow engineered into the system, so that atoms hopping around an ...
7
votes
1answer
178 views

Relations between diffeomorphism symmetry theories and invariant $SU(N), N \rightarrow \infty$ theories

Is it possible to have, an exhaustive panorama (as much as possible), about the relations between theories having a diffeomorphism symmetry, and theories having a $SU(N), N\rightarrow\infty$ ...
5
votes
1answer
155 views

Unitary gauge for non-abelian case

I'm reading Chapter 19 of Mandle and Shaw's Quantum field theory. In the first section it is explained that one can go with a $SU(2)$ followed by a $U(1)$ transformation from $$\begin{bmatrix}\eta_1(x)...
3
votes
1answer
76 views

What is the importance of vector potential not being unique?

For a magnetic field we can have different solutions of its vector potential. What is the physical aspect of this fact? I mean, why the nature allows us not to have an unique vector potential of a ...
1
vote
1answer
141 views

Why are string theorist so indifferent to the gauge structure of gravity? [closed]

Gravity shares many of the characteristics of Yang-Mills gauge theory. For example, the affine connection plays the similar role as the gauge potential in gauge theory, the Riemann tensor plays the ...
4
votes
1answer
154 views

What is the relationship between BRST symmetry and gauge symmetry?

As far as i know the BRST symmetry is an infinitesimal (and expanded) version of gauge symmetry. Recently I read the following: "when QFT was reformulated in fiber bundle language for application to ...
0
votes
0answers
39 views

What's the relation between representation theory and mass / electric charge?

This is a follow-up on this answer, where ACuriousMind wrote Formally, both the mass and the charge classify certain irreducible representations of the Poincaré group and the circle group, ...
0
votes
1answer
22 views

Gauge transformation of wave function of a system of stationary charges

Let's say we have a system of $n$ stationary charges interacting via Coulomb potential. Let's ignore possible external electromagnetic fields. Moreover the system is quantum, and its wave function is $...
1
vote
1answer
54 views

Derivation Of The Equation Of Motion Of String from Polyakov action

I'm stuck at a step in the derivation of the equations of motions of a string using the Polyakov action. In Polchinski's textbook in String Theory , Page 14 ; Equation ( 1.2.25 ) , Varying the ...
0
votes
1answer
49 views

What is the meaning of 'physical gauge'?

What does it mean for a gauge to be a physical gauge in your gauge choice of the theory, and why is it called the "physical gauge"?
6
votes
1answer
113 views

Hamiltonian and Energy of a charged particle in an Electromagnetic field

The Lagrangian of a charged particle of charge $e$ moving in an electromagnetic field is given by $$L=\frac{1}{2}m\dot{\textbf{r}}^2-e\phi-e\textbf{A}\cdot \textbf{v}$$ where $\phi(\textbf{r},t)$ is ...
5
votes
2answers
3k views

Gauge Invariance of the Hamiltonian of the electromagnetic field

The Hamiltonian for an electron of mass $m$ and charge $e$ in an exterior electromagnetic field is $$H=\frac{1}{2m}(p-(e/c)A)^2+e\varphi.$$ The corresponding (via canonical quantization) quantum ...
0
votes
1answer
43 views

Coupling constant in the Yang-Mills action

Intuitively, gauge coupling defines the strength of interactions between fields. But how to interpret the coupling $1/g^2$ in front of the kinetic term of Yang-Mills theories, $-\frac{1}{4g^2}tr(F_{\...
1
vote
1answer
76 views

Some questions about gauge theory

Let's talk quantum mechanics. I have a charged particle moving on a sphere. It has a wave function $\psi$. At time $t=0$, there is no magnetic flux piercing the sphere. Instantaneously, I introduce a ...
1
vote
1answer
68 views

Magnetic vector potential of an infinite wire

Using the integral $$A=\frac{\mu_0}{4 \pi} \int \frac{I \vec{dl}}{r}$$ for calculating magnetic vector potential of an infinite wire we get $$A = \left(\frac{\mu_0 I}{4 \pi}\right) \ln(\sec \theta + \...
0
votes
0answers
43 views

Gravity as a gauge theory - Cartan-Killing form?

First, let me state the form of Lagrangian for YM and GR \begin{align} L_{YM} = \alpha \textrm{tr}(F^2), \qquad L_{GR} = \beta R \end{align} I heard, YM is a gauge theory but GR isn't a really gauge ...