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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4
votes
1answer
169 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 ...
3
votes
1answer
553 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
210 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
601 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 ...
4
votes
2answers
647 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 ...
5
votes
1answer
353 views

Taking the continuum limit of $U(N)$ gauge theories

I would like to draw your attention to appendix $C$ on page 38 of this paper. The equation $C.2$ there seems to be evaluating the sum $\sum_R \chi _R (U^m)$ in equation 3.16 of this paper. I ...
3
votes
1answer
256 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
1answer
345 views

Why are all observable gauge theories not vector-like?

Why are all observable gauge theories not vector-like? Will this imply that the electron and/or fermions do not have mass? How is this issue resolved? Background: The Standard Model is a ...
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 ...
2
votes
1answer
470 views

Wilson loops and gauge invariant operators (Part 1)

I guess the Hilbert space of the theory is precisely the space of all gauge invariant operators (mod equations of motion..as pointed out in the answers) Is it possible that in a gauge theory the ...
6
votes
1answer
551 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 ...
0
votes
2answers
134 views

Is the Chern-Simons integral of gauge fields over black hole singularities zero?

Suppose we have an evaporating black hole and a nonabelian Yang-Mills theory with a $\theta$ topological term. This counts the total number of instantons minus antiinstantons. Consider the total ...
6
votes
3answers
888 views

Gauge fixing choice for the gauge field $A_0$

In many situations, I have seen that the the author makes a gauge choice $A_0=0$, e.g. Manton in his paper on the force between the 't Hooft Polyakov monopole. Please can you provide me a ...
2
votes
1answer
81 views

How do we deal with Gribov ambiguities when calculating in quantum gauge theories?

How do we deal with Gribov ambiguities when actually calculating in quantum gauge theories? Any literature references?
4
votes
1answer
582 views

Noether current for the Yang-mills-higgs lagrangian

I am trying to calculate the Noether's current, more specifically, the energy density of the Yang-mills-Higgs Lagrangian. Please refer to the equations in the Harvey lectures on Magnetic Monopoles, ...
1
vote
1answer
245 views

What is the winding number of a magnetic monopole, and why is it conserved

I had asked a similar question about a calculation involving the winding number here. But i haven't got a satisfactory response. So, I am rephrasing this question in a slightly different manner. What ...
5
votes
2answers
527 views

Winding number in the topology of magnetic monopoles

I am reading on magnetic monopoles from a variety of sources, eg. the Jeff Harvey lectures.. It talks about something called the winding $N$, which is used to calculate the magnetic flux. I searched ...
5
votes
0answers
84 views

How do you simulate a quantum gauge theory in a gauge with negative norms on a quantum computer?

How do you simulate a quantum gauge theory in a gauge with negative norms on a quantum computer? There are some gauges with negative norms. It's true that if restricted to gauge invariant states, the ...
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
0answers
570 views

The meaning of Goldstone boson equivalence theorem

The Goldstone boson equivalence theorem tells us that the amplitude for emission/absorption of a longitudinally polarized gauge boson is equal to the amplitude for emission/absorption of the ...
4
votes
1answer
214 views

Gauge symmetry description for $\phi^4$?

That is a follow-up to this question: Gauge symmetry is not a symmetry? Ok, gauge symmetry is not a symmetry, but ... ... a redundancy in our description, by introducing fake degrees of freedom ...
5
votes
2answers
134 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 ...
2
votes
2answers
278 views

What evidence is there for the electroweak higgs mechanism?

The wikipedia article on the Higgs mechanism states that there is overwhelming evidence for the electroweak higgs mechanism, but doesn't then back this up. What evidence is there?
6
votes
0answers
246 views

Is the U(1) gauge theory in 2+1D dual to a U(1) or an integer XY model?

The compact U(1) lattice gauge theory is described by the action $$S_0=-\frac{1}{g^2}\sum_\square \cos\left(\sum_{l\in\partial \square}A_l\right),$$ where the gauge connection $A_l\in$U(1) is defined ...
1
vote
1answer
975 views

Yukawa Coupling of a Scalar $SU(2)$ Triplet to a Left-Handed Fermionic $SU(2)$ Doublet

Suppose we have a field theory with a single complex scalar field $\phi$ and a single Dirac Fermion $\psi$, both massless. Let us write $\psi _L=\frac{1}{2}(1-\gamma ^5)\psi$. Then, the Yukawa ...
26
votes
0answers
273 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 ...
5
votes
2answers
676 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 $$ ...
4
votes
1answer
459 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 ...
7
votes
2answers
460 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 ...
9
votes
1answer
544 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 ...
3
votes
0answers
187 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 ...
4
votes
1answer
295 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
322 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 ...
10
votes
0answers
695 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 ...
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. ...
3
votes
1answer
252 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 ...
-4
votes
3answers
866 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 ...
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 ...
6
votes
2answers
383 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
4answers
980 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 ...
2
votes
1answer
611 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 ...
7
votes
2answers
225 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
355 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
414 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
1answer
562 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 ...
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 ...
2
votes
1answer
407 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 ...
13
votes
4answers
709 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 ...