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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13
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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
348 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
145 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
177 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
577 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
272 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
312 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. ...
2
votes
1answer
497 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?
5
votes
2answers
488 views

Gauge fixing and equations of motion

Consider an action that is gauge invariant. Do we obtain the same information from the following: Find the equations of motion, and then fix the gauge? Fix the gauge in the action, and then find the ...
5
votes
1answer
175 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 ...
2
votes
3answers
187 views

Quantizing first-class constraints for open algebras: can Hermiticity and noncommutativity coexist?

An open algebra for a collection of first-class constraints, $G_a$, $a=1,\cdots, r$, is given by the Poisson bracket $\{ G_a, G_b \} = {f_{ab}}^c[\phi] G_c$ classically, where the structure constants ...
3
votes
1answer
555 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 ...
3
votes
1answer
209 views

For nonabelian Yang-Mills in the Coulomb phase, can soft gluons render the charge orientation of charged particles indefinite?

For nonabelian Yang-Mills in the Coulomb phase, can soft gluons render the charge orientation of charged particles indefinite? Let's say the gauge group is a nonabelian simple Lie group G. Suppose ...
3
votes
2answers
144 views

What exactly is the weak portion of the SM gauge group?

This Wikipedia article: http://en.wikipedia.org/wiki/Left%E2%80%93right_symmetry states that the weak part of the SM gauge group is not $SU(2)_L \times U(1)_Y$ but $ \frac{ SU(2)_L \times ...
4
votes
2answers
650 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 ...
3
votes
4answers
823 views

First class and second class constraints

Hello I am working on a project that involves the constraints. I checkout the paper of Dirac about the constraints as well as some other resources. But still confuse about the first class and second ...
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
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 ...
4
votes
1answer
589 views

Wilson loops and gauge invariant operators (Part 2)

These questions are sort of a continuation of this previous question. I would like to know of the proof/reference to the fact that in a pure gauge theory Wilson loops are all the possible gauge ...
6
votes
3answers
891 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 ...
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 ...
2
votes
1answer
471 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 ...
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 ...
2
votes
1answer
159 views

Is there any good gauge-fixing prescription for discrete gauge symmetries?

Nearly all gauge-fixing prescriptions are based upon setting some function involving the gauge fields to be zero. That function is continuous and varies over the real/complex numbers. Trying the same ...
6
votes
2answers
173 views

Are timelike diffeomorphisms really redundancies in description in quantum gravity?

Are timelike diffeomorphisms really redundancies in description in quantum gravity? Certainly Yang-Mills gauge transformations can be considered redundancies in description. Ditto for p-form ...
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?
3
votes
1answer
227 views

Using the covariant derivative to find force between 't Hooft-Polyakov magnetic monopoles

I am reading this research paper authored by NS Manton on the Force between 't Hooft-Polyakov monopoles. I have a doubt in equation 3.6 and 3.7. We assume the gauge field for a slowly accelerating ...
4
votes
1answer
583 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, ...
5
votes
3answers
311 views

Could general relativity and gauge theories in principle be covered in one course?

It's always nice to point out the structural similarieties between (semi-)Riemannian geometry and gauge field theories alla Classical yang Mills theories. Nevertheless, I feel the relation between the ...
3
votes
2answers
482 views

What is the ontological status of Faddeev Popov ghosts?

We all know Faddeev-Popov ghosts are needed in manifestly Lorentz covariant nonabelian quantum gauge theories. We also all know they decouple from the rest of matter asymptotically, although they ...
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 ...
3
votes
3answers
810 views

Counting degrees of freedom of gauge bosons

Gauge bosons are represented by $A_{\mu}$, where $\mu = 0,1,2,3$. So in general there are 4 degrees of freedom. But in reality, a photon (gauge boson) has two degrees of freedom (two polarization ...
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 ...
5
votes
2answers
528 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 ...
4
votes
0answers
571 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 ...
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
248 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 ...
9
votes
1answer
426 views

How to determine if an emergent gauge theory is deconfined or not?

2+1D lattice gauge theory can emerge in a spin system through fractionalization. Usually if the gauge structure is broken down to $\mathbb{Z}_N$, it is believed that the fractionalized spinons are ...
1
vote
1answer
979 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 ...
5
votes
2answers
678 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 $$ ...