The tag has no usage guidance.

learn more… | top users | synonyms

23
votes
1answer
2k views

What does it mean that there is no mathematical proof for confinement?

I see this all the time* that there still doesn't exist a mathematical proof for confinement. What does this really mean and how would a sketch of a proof look like? What I mean by that second ...
8
votes
3answers
2k views

Gravity as a gauge theory

Currently, (classical) gravity (General Relativity) is NOT a gauge theory (at least in the sense of a Yang-Mills theory). Why should "classical" gravity be some (non-trivial or "special" or ...
12
votes
2answers
663 views

Yang-Mills CP violation

Why does a term proportional to $\left(F,\,\tilde{F}\right)\propto Tr\left[ F_{\mu\nu}\tilde{F}^{\mu\nu}\right]$ in the Lagrangian of the pure Yang-Mills theory violate CP?
4
votes
2answers
307 views

How many physical degrees of freedom does the $\mathrm{SU(N)}$ Yang-Mills theory have?

The $\mathrm{U(1)}$ QED case has two physical degrees of freedom, which is easy to understand because the free electromagnetic field must be transverse to the direction of propagation. But what are ...
14
votes
1answer
573 views

Spontaneous breaking of Lorentz invariance in gauge theories

I was browsing through the hep-th arXiv and came across this article: Spontaneous Lorentz Violation in Gauge Theories. A. P. Balachandran, S. Vaidya. arXiv:1302.3406 [hep-th]. (Submitted on 14 ...
6
votes
1answer
686 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 ...
13
votes
0answers
381 views

What is Motivic mathematics and how is it used in physics?

In a few videos I've seen where he discusses the new approach to calculating the super Yang Mills scattering amplitudes, Nima Arkani-Hamed sometimes alludes to the use of Motivic methods as being ...
7
votes
1answer
352 views

Intersecting Wilson loops in 2D Yang-Mills

I am currently trying to understand 2D Yang-Mills theory, and I cannot seem to find an explanation for calculation of the expectation value of intersecting Wilson loops. In his On Quantum Gauge ...
7
votes
1answer
355 views

Wightman axioms and gauge symmetries

I have a basic understanding of the Wightman axioms for QFT. I was reading the about the Mass Gap problem for simple compact gauge groups and was wondering how the gauge group is supposed to be ...
6
votes
2answers
184 views

Gauge fields and strings: Loop equations

I am trying to derive Eq. (7.25) (p. 117) of Polyakov's book: $$ \delta \Psi (C) = \int_{0}^{2\pi} {\rm P} \left(F_{\mu\nu}(x(s)) \exp \oint_C A_\mu dx^\mu \right)\dot{x}_\nu \delta x_\mu(x) \, {\rm ...
6
votes
2answers
487 views

Can auxiliary fields be thought of as Lagrange multipliers?

In the BRST formalism of gauge theories, the Lautrup-Nakanishi field $B^a(x)$ appears as an auxiliary variable $$\mathcal{L}_\text{BRST}=-\frac{1}{4}F_{\mu\nu}^a F^{a\,\mu\nu}+\frac{1}{2}\xi B^a B^a + ...
4
votes
3answers
491 views

Problems with putting mass on Yang-Mills theory by hand

When Yang-Mills field theory was introduced, a problem is that the gauge invariance can not allow mass for the gauge field. Later people invented spontaneous symmetry breaking and Higgs mechanism to ...
8
votes
1answer
207 views

Boundary currents for Asymptotic Symmetry Group (ASG)

In the context of asymptotic symmetry groups, what is a boundary current? Why is it called a "current"? Context: I'm reading Strominger's recent paper on Asymptotic symmetry group of Yang-Mills ...
7
votes
1answer
250 views

Reference for the ${\cal N}=3$ Chern-Simons Lagrangian at general $N_c$, $N_f$

I was wondering if someone could give me a reference where someone has explicitly written the Lagrangian for ${\cal N}=3$ $SU(N_c)$ Chern-Simons theory coupled to $N_f$ fundamental hypermultiplets. ...
5
votes
1answer
164 views

Why is the Yang-Mills Comparator unitary?

In chapter 15.2 of Peskin, the comparator is defined, as some object $U\left(y,\,x\right)$ which transforms as: $$ U\left(y,\,x\right) \mapsto V\left(y\right) U\left(y,\,x\right) ...
5
votes
1answer
395 views

Field strength vanishes iff $A_{\mu}$ is pure gauge

Is it true that the field strength $F_{\mu\nu}$ in a non-Abelian gauge theory with gauge group $G$ vanishes if, and only if, the gauge field $A_{\mu}$ is a pure gauge? I can show one implication. ...
4
votes
1answer
656 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 ...
3
votes
1answer
158 views

Unconstrained action in Yang-Mills theory

Is there any gauge in which Yang-Mills theory (4d, non-SUSY) can be written as a local action containing only the propagating modes?
2
votes
1answer
226 views

Lagrangian depends on second derivative of field

In case of the gauge-fixed Faddeev-Popov Lagrangian: $$ \mathcal{L}=-\frac{1}{4}F_{\mu\nu}\,^{a}F^{\mu\nu ...
2
votes
1answer
558 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 ...
7
votes
1answer
475 views

Hodge star operator on curvature?

I've a question regarding the Hodge star operator. I'm completely new to the notion of exterior derivatives and wedge products. I had to teach it to myself over the past couple of days, so I hope my ...
6
votes
3answers
1k 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 ...
3
votes
1answer
127 views

Yang-Mills constraints and Poisson brackets

Let's have constraints for Yang-Mills theory: $$ \varphi_{a} = \partial_{i}\pi^{i}_{a} - f_{abc}\pi^{b}_{i}A^{c}_{i}. $$ I have read the statement that $$ \tag 1 [\varphi_{a}(\mathbf x), ...
3
votes
1answer
246 views

How can “quantum particles have positive masses, even though the classical waves travel at the speed of light”?

Clay Mathematics Institute writes about the Yang-Mills and mass gap problem on this page http://www.claymath.org/millennium/Yang-Mills_Theory/: The successful use of Yang-Mills theory to describe ...
0
votes
2answers
162 views

Reasons for choosing $SU(3)$ as the color group vs. $SO(4)$

What are the reasons that $SU(3)$ is used for QCD? Why wouldn't the simpler & smaller group $SO(4)$ make a better candidate?
2
votes
1answer
523 views

Spontaneous symmetry breaking and 't Hooft and Polyakov monopoles

What is spontaneous symmetry breaking from a classical point of view. Could you give some examples, using classical systems.I am studying about the 't Hooft and Polyakov magnetic monopoles solutions, ...