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1
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0answers
27 views

What happens to large gauge transformations in gauges different from the temporal gauge?

There are already several questions regarding the meaning and definition of large gauge transformations. Discussions of large gauge transformations typically only happen in the context of the ...
2
votes
1answer
74 views

$U(N)$ & $SU(N)$ : What's the conceptual difference in Gauge Theory?

I know the mathematical difference that one means $ absolutevalue(det) = 1$ and one means det = 1 (rotation) and that ones the subgroup of the other and so on. But: has a local/gauged $SU(3)$ ...
3
votes
0answers
104 views

A Naive Question about Gauge Theory

I am suffering from a question I encountered from the lecture notes of gauge theory by David Tong. The problem comes from page 67 on the gauge fixing in back-ground gauge method. In David Tong's ...
0
votes
1answer
114 views

Why quarks in the fundamental and gluons in the adjoint?

I have been told that in gauge theories “fermionic matter goes in the fundamental rep of $SU(N)$, while gauge fields go in the adjoint rep”. I understand how this works, and for instance, in QCD,...
0
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0answers
72 views

Wilson loop and Polyakov loop

As I understand, the Wilson line is the operator $W(x) = P\exp(i\int_{xi}^{xf} A.dx)$, where $P$ is path ordering. The Polyakov loop $P(x)$ on the other hand is the trace of the Wilson loop $W(x)$ ...
0
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0answers
85 views

QCD vs. QED gauge invariance

Trying to understand the difference between QED and QCD gauge invariance treatment I found the following paper: https://arxiv.org/pdf/1101.3425.pdf I have the following questions: 1) I understand Eq....
2
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1answer
149 views

Invariance of Yang-Mills Lagrangian under charge conjugation

The Yang-Mills Lagrangian gauge invariant under an $SU(N)$ tranformation can be written as $${\cal L} = -\frac{1}{4}F_{\mu\nu}^i F^{i\ \mu\nu} \tag1$$ (Sum over $i$ implicit) This Lagrangian ...
3
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0answers
54 views

What is the relation between the Gribov problem and color confinement?

I have heard that the Gribov problem is in some way related to color confinement (For instance: Gribov copies and confinement). Although I understand what both the Gribov and confinement problems are, ...
1
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1answer
79 views

Isn't there a unique vacuum of the Yang-Mills quantum theory?

The theta vacua$^1$ of a Yang-Mills quantum theory are given by $$|\theta\rangle=\sum\limits_{n=-\infty}^{\infty}e^{in\theta}|n\rangle.$$ In Srednicki's Quantum Field Theory, he claims that the ...
3
votes
1answer
156 views

What is the Noether charge associated with the the color $SU(3)$ symmetry of QCD?

A version of the Noether's theorem applies to local gauge symmetries. What is the Noether's charge associated with a non-abelian gauge symmetry such as the color $SU(3)$ and how is that derived? I ...
1
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0answers
43 views

Showing that $U(1)_R$ charge is non-anomalous in SUSY QCD when $r=\frac{F-N}{F}$

I'm trying to show that the value of the R-charge $r$ for which the R-symmetry is non-anomalous is given by $r=\frac{F-N}{F}$. To do this we must calculate the triangle diagrams for the quarks $\...
3
votes
1answer
148 views

What is the effect of including additional representations in the action of a lattice gauge theory?

I'm reading Introduction to Quantum Fields on a Lattice by Jan Smit. When introducing the lattice gauge-field action as a sum over plaquettes, Smit says that in general the action should include a sum ...
4
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0answers
85 views

Which of the Wightman axioms are not incorporated by four dimensional quantum Yang-Mills?

I am trying to understand the quantum Yang-Mills existence problem but the best I have seen so far is the statement that there is no known interacting relativist field theory in four dimensions which ...
3
votes
1answer
69 views

QCD from chirally segregated, gauged $SU(3)_L \times SU(3)_R$?

There are already theory papers out there in which color $SU(3)_C$ is actually the diagonal subgroup of multiple $SU(3)$ factors. But due to a comment by @zooby, a new twist on this idea occurred to ...
1
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0answers
62 views

Why is $SU(3)$ and not $U(3)$ the correct gauge symmetry? [duplicate]

If quarks come in three colours $r$, $g$ and $b$ than (neglecting all other quantum numbers and spacial freedom for now) a state of a quark would be a vector in $\mathbb{C}^3$. If we are now looking ...
3
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0answers
206 views

Is the physical mass of the electron a gauge invariant quantity?

In Lattice, one cannot calculate gauge non-invariant quantities, such as the quark mass. This is because one averages over the gauge and gets 0. One way to get around the issue is to fix the gauge. ...
2
votes
1answer
88 views

What is the physical meaning of the Gell-Mann matrices generating SU(3)?

I understand on a surface level that there are these matrices that generate the group SU(3). However, when reading books on gauge theory they appear to make the jump from SU(3) having 8 generators to ...
0
votes
1answer
62 views

If the $SU(3)$ Noether charge is not gauge-invariant how can we say Hadrons are colorless?

The Noether charge associated with global $SU(3)$ invariance is \begin{equation} J^{\mu}_a=-f_{abc}F_c^{\nu\mu}A_{b\mu}-i\frac{\delta \mathcal{L}_{Matter}}{\delta D_{\nu}\psi}t_a\psi \end{equation} ...
6
votes
1answer
397 views

(Anti)commutation of ghosts and fermions

I would like to ask whether fermionic Grassmann fields in a gauge theory path integral (say in QCD) should be chosen to commute or anticommute with ghost and anti-ghost fields. The way most textbooks ...
3
votes
1answer
372 views

Gauge invariance of $\theta$-term in QCD

I have a problem with the $\theta$-term in the QCD-Lagrangian $$ \mathcal{L} = \overline{q}(x)i\gamma_\mu{D^\mu} q(x)-\overline{q}(x)\mathcal{M}q-\frac{1}{4}F^a_{\mu\nu}F_a^{\mu\nu}+ \theta \frac{g^...
4
votes
1answer
386 views

Axial anomaly in QCD VS axial anomaly in current algebra QCD

I would like to understand the distinction between an axial anomaly in QCD (Theta Vacuum: axion -> 2 gluons) and an axial anomaly in QCD of current (Chern–Simons term: pion->two photons, photon->three ...
1
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0answers
36 views

The remained global flavor symmetries of massless quarks after gauging electromagnetic $U(1)$

For $N_f$ numebr of massless quarks, we know that there are global symmetries $$ \frac{SU(N_f)_L \times SU(N_f)_R \times U(1)_V}{Z_{N_f}} $$ here $U(1)_V$ is the same as $U(1)$-Baryon number ...
7
votes
0answers
184 views

Non-abelian string in QCD?

It is easy to find various/many papers in HEP-lattice talk about "Non abelian string in QCD". What does it mean to say "non abelian string in QCD?" Does "non abelian string" happen for pure Yang-...
4
votes
1answer
363 views

Why is the temporal gauge $A_0=0$ so popular in discussions of non-perturbative effects?

Almost every discussion of non-perturbative effects in Yang-Mills theory mentions in passing that they work in the temporal gauge. Why is this the case? A good example is the QCD vacuum. Almost ...
2
votes
1answer
530 views

The logic of large $N$ expansion

I have some understanding of how the large-$N$ expansion works but feel like I'm missing the most important concepts. For example, I understand that in QCD the order of the diagram in $N$ depends ...
8
votes
0answers
292 views

Is the QCD Lagrangian without a $\theta$-term invariant under large gauge transformations?

In his book "Quantum field theory", Kerson Huang states that we need to add the term $$\frac{i\theta}{32\pi^2}G_{\mu\nu}^a \tilde{G}_{\mu\nu}^a$$ to the Lagrangian, to make it invariant under large ...
3
votes
1answer
140 views

How many glueballs are there?

As I understand there are eight types of gluons (linear combinations of color/anticolor pairs with varying amplitudes) which can combine (for very short periods) to form glueballs. If there were no ...
1
vote
1answer
115 views

Why group elements associated with gauge transformations of finite action field configurations in QCD don't depend in $r$?

I am reading the chapter on instantons in Coleman's Aspects of Symmetry. I am puzzled by an argument i don't quite follow. In section 3.2, Coleman considers configurations of the gauge field with ...
8
votes
1answer
1k views

Polarization Sums in QCD for the calculation of parton model splitting functions

Before i state the actual problem, here's a premise. In the case of a Spin 1 massive particle it's possible to demonstrate that $$\sum_{\lambda=0,\pm1}\epsilon_{\lambda}^{* \ \mu}\epsilon_{\lambda}^{\...
7
votes
2answers
360 views

Is there some no-go theorem for $D=9$ Kaluza Klein QCD+EM?

While QCD is a typical product of AdS/CFT and some other research trends in extra dimensions, I have never found in the literature an example producing the non-chiral part of the standard model, ...
6
votes
1answer
323 views

Massive Gauge Bosons without Higgs fields

In a possible theory like our Standard model but without a Higgs i.e.: $$ \mathcal{L}=i\bar{\Psi}_f\gamma_\mu D^\mu\Psi_f-\text{Tr}[G^b_{\mu\nu}G^{b\,\mu\nu}] $$ where $b,f$ run over the typical ...
8
votes
0answers
156 views

Why does strong interaction increase with distance?

I read numerous times that strong interaction increases with distance. But how can one actually derive the force-distance relation from the lagrangian (quark field + gluon field + gauge coupling)? ...
7
votes
1answer
331 views

Does the LSZ reduction method prove gauge-independence in massless gauge theories?

I've been working my way through L. Baulieu's excellent paper [Perturbative gauge theories, Physics Reports, Volume 129, Issue 1, December 1985, Pages 1-74]. Towards the end, he goes on to prove that ...
12
votes
1answer
3k views

How to Perform Wick Rotation in the Lagrangian of a Gauge Theory (like QCD)?

I'm studying Lattice QCD and got stuck in understanding the process of going from a Minkowski space-time to an Euclidean space-time. My procedure is the following: I considered the Wick rotation in ...
11
votes
2answers
2k views

Why is color conserved in QCD?

According to Noether's theorem, global invariance under $SU(N)$ leads to $N^2-1$ conserved charges. But in QCD gluons are not conserved; color is. There are N colors, not $N^2-1$ colors. Am I ...
6
votes
1answer
633 views

Weak isospin and types of weak charge

My understanding is that QCD has three color charges that are conserved as a result of global SU(3) invariance. What about SU(2) weak? Does it have two types of charges? What I'm getting at is: U(1) -...
2
votes
1answer
245 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 $U(x)$ $$|\psi\rangle\...
6
votes
1answer
1k 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 ...
9
votes
4answers
3k 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 ...
6
votes
1answer
108 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 "...
4
votes
1answer
972 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 ...