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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17
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1answer
276 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
154 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 ...
64
votes
4answers
5k 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
532 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
600 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
381 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
939 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
223 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
346 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
404 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) ...
-4
votes
3answers
837 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
546 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
483 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 ...
2
votes
1answer
591 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 ...
2
votes
1answer
401 views

Single trace partition function

I would be glad if someone can help me understand the argument in appendix B.1 and B.2 (page 76 to 80) of this paper. The argument in B.1 supposedly helps understand how the authors in that paper ...
15
votes
1answer
1k views

Diff(M) as a gauge group and local observables in theories with gravity

In a gauge theory like QED a gauge transformation transforms one mathematical representation of a physical system to another mathematical representation of the same system, where the two mathematical ...
6
votes
1answer
539 views

Modes of a QFT and irreducible representation of the gauge group

This is in reference to the calculation in section 3.3 starting page 20 of this paper. I came across an argument which seems to say that the "constraint of Gauss's law" enforces gauge theory on ...
4
votes
2answers
1k views

What's the point of having an einbein in your action?

One often comes across actions written with an extra auxiliary field, with respect to which if you vary the action, you get the equation of motion of the auxiliary field, which when plugged into the ...
21
votes
2answers
2k views

Is there a T-dual of Witten's twistor topological string theory?

In late 2003, Edward Witten released a paper that revived the interest in Roger Penrose's twistors among particle physicists. The scattering amplitudes of gluons in $N=4$ gauge theory in four ...
6
votes
6answers
627 views

Interaction ranges in the Standard Model - Electrodynamics vs QCD

as you might know, the Standard Model of physics can be seen as a $U(1)\times SU(2)\times SU(3)$ gauge theory where each symmetry group accounts for different force fields. The behaviour for the ...
12
votes
4answers
693 views

Nonlinear optics as gauge theory

the widely used approach to nonlinear optics is a Taylor expansion of the dielectric displacement field $\mathbf{D} = \epsilon_0\cdot\mathbf{E} + \mathbf{P}$ in a Fourier representation of the ...
5
votes
2answers
869 views

Decomposition of a vectorial field in free-curl and free-divergence fields

Is it always possible to do that decomposition? I'm asking it because Helmholtz theorem says a field on $\mathbb{R}^3$ that vanishes at infinity ($r\to \infty$) can be decomposed univocally into a ...