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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5
votes
2answers
811 views

The Faddeev-Popov Lagrangian

This is a non-abelian continuation of this QED question. The Lagrangian for a non-abelian gauge theory with gauge group $G$, and with fermion fields and ghost fields included is given by $$ ...
6
votes
4answers
1k views

What's the distinctions between Yang-Mills theory and QCD?

So Yang-Mills theory is a non-abelian gauge theory, and we used a lot in QCD calculation. But what are the distinctions between Yang-Mills theory and QCD? And distinctions between supersymmetric ...
4
votes
1answer
552 views

QED BRST Symmetry

This is a homework problem that I am confused about because I thought I knew how to solve the problem, but I'm not getting the result I should. I'll simply write the problem verbatim: "Consider QED ...
2
votes
1answer
47 views

Time Evolution of a Manifold Embedding

Given a smooth manifold $\mathcal{M}$ with a simplicial complex embedding $\mathsf{S}$, what specific tools or methods can be used to give an analysis of the time evolution of the manifold given some ...
7
votes
2answers
512 views

Why do we like gauge potentials so much?

Today I read articles and texts about Dirac monopoles and I have been wondering about the insistence on gauge potentials. Why do they seem (or why are they) so important to create a theory about ...
2
votes
2answers
271 views

Gauge invariant scalar potentials

If $\Phi$ is a multi-component scalar field which is transforming in some representation of a gauge group say $G$ then how general a proof can one give to argue that the potential can only be a ...
4
votes
1answer
476 views

Gauge invariance and the form of the Rarita-Schwinger action

in Weinberg Vol. I section 5.9 (in particular p. 251 and surrounding discussion), it is explained that the smallest-dimension field operator for a massless particle of spin-1 takes the form of a field ...
6
votes
4answers
389 views

Can an Electromagnetic Gauge Transformation be Imaginary?

The Hamiltonian of a non-relativistic charged particle in a magnetic field is $$\hat{H}~=~\frac{1}{2m} \left[\frac{\hbar}{i}\vec\nabla - \frac{q}{c}\vec A\right]^2$$. Under a gauge transformation ...
3
votes
0answers
191 views

Attempts to explain Higgs coupling as a gauge transformation symmetry

As is (supposedly) well known, Electromagnetic coupling can be "explained" as a closure term to a langrangian comprising a free Dirac field and a free vector field that are required to be invariant ...
7
votes
2answers
796 views

How does non-Abelian gauge symmetry imply the quantization of the corresponding charges?

I read an unjustified treatment in a book, saying that in QED charge an not quantized by the gauge symmetry principle (which totally clear for me: Q the generator of $U(1)$ can be anything in ...
4
votes
1answer
339 views

SU(2) yang-mills EOM

I'm just playing around tonight trying to better myself, but I'm having trouble with some indices on my yang-mills lagrangian. I have a gauge group $SU(2)$ and a field strength tensor $$ ...
6
votes
1answer
336 views

Can a photon see ghosts?

Does it make sense to introduce Faddeev–Popov ghost fields for abelian gauge field theories? Wikipedia says the coupling term in the Lagrangian "doesn't have any effect", but I don't really know ...
6
votes
2answers
266 views

Gauge invariance and Bohm-Aharonov effect

I am confused with the Bohm-Aharonov effect: though quantum mechanics is said to be gauge invariant, the presence of a solenoid imposes a gauge. I used to think that a phase shift did not change ...
8
votes
2answers
154 views

Torsion and gauge invariant EM kinetic term

Everytime I hear about adding torsion to GR, something struggles me: how do you create a kinetic term for the electromagnetic field that is still gauge-invariant? One of the consequences of torsion is ...
8
votes
2answers
1k views

Wilson/Polyakov loops in Weinberg's QFT books

I wanted to know if the discussion on Wilson loops and Polyakov loops (and their relationship to confinement and asymptotic freedom) is present in the three volumes of Weinberg's QFT books but in some ...
6
votes
1answer
113 views

How does a geodesic equation on an n-manifold deal with singularities?

My general premise is that I want to investigate the transformations between two distinct sets of vertices on n-dimensional manifolds and then find applications to theoretical physics by: ...
12
votes
0answers
836 views

Gauge redundancies and global symmetries

It is often said that local (gauge) transformation is only redundancy of description of spin one massless particles, to make the number degrees of freedom from three to two. It is often said that ...
12
votes
1answer
498 views

What is a “free” non-Abelian Yang-Mill's theory?

I hope this question will not be closed down as something completely trivial! I did not think about this question till in recent past I came across papers which seemed to write down pretty much ...
35
votes
0answers
1k views

On the Coulomb branch of N=2 supersymmetric gauge theory

The chiral ring of the Coulomb branch of a 4D $N=2$ supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the Casimirs are ...
1
vote
0answers
73 views

Reference request: Introductions to current mathematics derived from / related to gauge theories (in physics) [duplicate]

I was searching for introductions to current mathematics derived from / related to gauge theories in physics. Can someone suggest some good references? E.g. Topics in Physical Mathematics by K. ...
5
votes
2answers
148 views

Is the distinction between the Poincaré group and other internal symmetry groups artificial?

For instance, given a theory and a formulation thereof in terms of a principal bundle with a Lie group $G$ as its fiber and spacetime as its base manifold, would a principle bundle with the Poincaré ...
5
votes
1answer
80 views

What does Gribov's last paper tell about coloured states?

In the first days of July 1997, after a long driving effort, crossing all of Europe to come to a meeting in Peñiscola, Vladimir Gribov fell fatally sick and he passed away one month later. His paper ...
13
votes
2answers
359 views

Normalization of the Chern-Simons level in $SO(N)$ gauge theory

In a 3d SU(N) gauge theory with action $\frac{k}{4\pi} \int \mathrm{Tr} (A \wedge dA + \frac{2}{3} A \wedge A \wedge A)$, where the generators are normalized to $\mathrm{Tr}(T^a ...
5
votes
1answer
520 views

Gauge invariance and Feynman path-integrals

Let me look at the Hamiltonian of a charged particle in a plane in a constant magnetic field ($\vec{B}$) pointing upwards - then in usual notation it is, $$\hat{H} = \frac{1}{2m}\biggl(\hat{p} + ...
8
votes
2answers
401 views

How to prove quantum N=4 Super-Yang-Mills is superconformal?

I'm especially interested in elegant illuminating proofs which don't involve a lot of straightforward technical computations Also, does a non-perturbative proof exist?
19
votes
4answers
851 views

Which exact solutions of the classical Yang-Mills equations are known?

I'm interested in the pure gauge (no matter fields) case on Minkowski spacetime with simple gauge groups. It would be nice if someone can find a review article discussing all such solutions EDIT: I ...
9
votes
1answer
932 views

Why should bosons be in the adjoint representation of the gauge group?

Is there a deep mathematical reason for why bosons should be in the adjoint representation of the gauge group rather than any other representation?
10
votes
1answer
405 views

Chern-Simons theory

In Witten's paper on QFT and the Jones polynomial, he quantizes the Chern-Simons Lagrangian on $\Sigma\times \mathbb{R}^1$ for two case: (1) $\Sigma$ has no marked points (i.e., no Wilson loops) and ...
13
votes
1answer
258 views

realization of: CFT generating fuction = AdS partition function

An important aspect of the AdS/CFT correspondence is the recipe to compute correlation functions of a boundary operator $\mathcal{O} $ in terms of the supergravity fields in the interior of the ...
13
votes
2answers
435 views

Topological twists of SUSY gauge theory

Consider $N=4$ super-symmetric gauge theory in 4 dimensions with gauge group $G$. As is explained in the beginning of the paper of Kapustin and Witten on geometric Langlands, this theory has 3 ...
9
votes
2answers
333 views

Is ghost-number a physical reality/observable?

One perspective is to say that one introduced the ghost fields into the Lagrangian to be able to write the gauge transformation determinant as a path-integral. Hence I was tempted to think of them as ...
11
votes
2answers
346 views

Gauge invariance for electromagnetic potential observables in test function form

This is a reference request for a relationship in quantum field theory between the electromagnetic potential and the electromagnetic field when they are presented in test function form. $U(1)$ gauge ...
29
votes
0answers
370 views

Systematic approach to deriving equations of collective field theory to any order

The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
3
votes
1answer
269 views

A loop quantum gravity toy inspired by an Aharonov-Bohm ring

Comparing my question to Give a description of Loop Quantum Gravity your grandmother could understand what I'm looking for here is a toy for a toddler ($\approx$ a pre-QFT graduate student). I seek ...
9
votes
1answer
57 views

Dual Pairs in Four Dimensions

Following the conversation here, I am wondering if anyone knows of an example of dual pair with 4-dimensional N=1 SUSY which relates a non-Abelian gauge theory on one side to a theory with a ...
17
votes
1answer
323 views

Models of higher Chern-Simons type

It has long been clear that (the action functional of) Chern-Simons theory has various higher analogs and variations of interest. This includes of course traditional higher dimensional Chern-Simons ...
12
votes
1answer
193 views

Are possible gauge fields in a Lagrangian theory always determined by the structure of the charged degrees of freedom?

An elementary example to explain what I mean. Consider introducing a classical point particle with a Lagrangian $L(\mathbf{q} ,\dot{\mathbf{q}}, t)$. The most general gauge transformation is $L ...
71
votes
5answers
8k views

Gauge symmetry is not a symmetry?

I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
9
votes
1answer
633 views

Discrete gauge theories

I'm trying to understand a particular case of gauge theories, namely discrete spaces on which a group G can act transitively, with a gauge group H which is discrete as well. From what I've already ...
11
votes
2answers
707 views

argument about fallacy of diff(M) being a gauge group for general relativity

I want to outline a solid argument (or bulletpoints) to show how weak is the idea of diff(M) being the gauge group of general relativity. basically i have these points that in my view are very solid ...
6
votes
2answers
399 views

Lagrangians combining terms with 1 and 2 derivatives

How are field theory Langrangians treated when some terms have 2 derivatives but others have only 1? Because the number of derivatives in a Lagrangian term is more easily even than odd, the ...
7
votes
5answers
1k views

proof of gauge invariance for quantum 1D ring

This is a question on gauge invariance in quantum mechanics. I do some simple math on a 1D wave-function with periodic boundary conditions, and get that gauge invariance is violated. What am I doing ...
7
votes
4answers
1k views

How many fundamental forces could there be?

We’re told that ‘all forces are gauge forces’. The process seems to start with the Lagrangian corresponding to a particle-type, then the application of a local gauge symmetry leading to the emergence ...
7
votes
2answers
230 views

Is there a meaning to the E,B analogues of other gauge fields?

From the gauge field $A_\mu$ and the QED lagrangian we can derive maxwell's equations in terms of electric and magnetic fields. Are there any situations where similar derivations using the other gauge ...
0
votes
1answer
389 views

What is the spectral energy density of virtual photons around a unit charge at rest?

Given that my previous question, namely "What is the number density of virtual photons around a unit charge?" has no precise answer, here is a more precise wording: What is the virtual photon ...
4
votes
2answers
453 views

Diff(M) and requirements on GR observables

This question is kind of inspired in this one: Diff(M) as a gauge group and local observables in theories with gravity The conundrum i'm trying to understand is how is derived the (quite) ...
-3
votes
3answers
979 views

What is physical in the principle of local gauge invariance? [closed]

Modern theories of interactions in particle physics are gauge ones. I know how the gauge fields are introduced in equations ($D = \partial + A$). I just do not see any physical motivation in it. I am ...
4
votes
1answer
617 views

What is “localisation” of instantons?

I often encountered the term "localization" in the context of instantons, as for example in the work of Nekrasov on extensions of Seiberg-Witten theory to N=1 gauge theories. Could someone give a ...
8
votes
2answers
612 views

Why do Faddeev-Popov ghosts decouple in BRST?

Why do Faddeev-Popov ghosts decouple in BRST? What is the physical reason behind it? Not just the mathematical reason. If BRST quantization is specifically engineered to make the ghosts decouple, how ...
3
votes
1answer
652 views

Lattice QCD and string theory

I've heard the claim that some aspects of string theory are used to improve Monte-Carlo simulations of lattice QCD, for example by people working at the LHC. I know a bit about Monte-Carlo methods in ...