All Questions
28
questions
0
votes
1
answer
59
views
Visualization of a gauge field with non-null winding number
In QCD you may add the term $\mathcal{L}_{\theta} = \theta\dfrac{g^2}{16\pi^2} \text{Tr}F\tilde{F}$, which turns out to be a total derivative. Now, it can be proven that the action of this lagrangian ...
- 1,611
5
votes
1
answer
267
views
Why is there only one coupling constant in Yang-Mills theory? Why are gluon self-coupling and gluon-matter coupling constants the same?
Is it non-trivial that the coupling constant $g$ in gluon self-interaction terms is the same as the coupling constant $g$ in gluon-fermion interaction term in Yang-Mills theory?
Pure Yang-Mills theory ...
- 192
9
votes
1
answer
1k
views
What is confinement?
I just got confused about the meaning of confinement in QFT.
The naive definition is that in QCD one cannot observe isolated quarks and gluons. This is a trivial statement because in any gauge theory ...
3
votes
0
answers
124
views
The 1-loop anomalous dimension of massless quark field for $SU(N)$ gauge theory with $n_f$ quark flavours
Considering $SU(N)$ gauge theory with $n_f$ massless quarks
I want to find the anomalous dimension to order of 1-loop of the massless quark field, that defined by: $$\gamma_q(g^{(R)})=\frac{1}{2Z_q}\...
0
votes
1
answer
108
views
Can a gauge theory with $SU(2)_{left}*SU(2)_{additional}$ symmetry contain confinement?
Consider a gauge theory with $SU(2)_{left}*SU(2)_{additional}$ symmetry.
By $additional$, I mean adding a new symmetry between an electron and a quark(like up quark and electron forming a doublet).
...
- 1,268
5
votes
1
answer
430
views
How do $\theta$-terms not violate gauge invariance?
In the context of QCD (and more generally, any quantum gauge theory in even dimensions), the $\theta$-term is
$$
\frac{\theta}{8\pi^2}\langle F_A\wedge F_A\rangle = \frac{\theta}{32\pi^2}\langle F_A^{\...
- 338
1
vote
0
answers
237
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Polyakov loops and Wilson loops as order parameters
At zero temperature, the confinement/deconfinement criterion is the area/length law of the following non-local parameter called the Wilson loop:
\begin{eqnarray}
W=\text{Tr}\exp\left(\oint_CA_idx^i\...
- 813
2
votes
0
answers
167
views
QCD generating functional and QCD vacuum from nonperturbative to perturbative regime!
The complete generating functional in QCD (starting from the most general renormalizable, Lorentz invariant and gauge invariant Lagrangian) given by $$Z_\theta[J]=\int \mathcal{D}A \exp i\int d^4x~ {\...
- 26.8k
1
vote
2
answers
424
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Why does QCD become strongly interacting at low energies and how low is low here?
A few days ago I asked a question about QCD chiral symmetry breaking and hopefully got a very good answer. But the problem is I am not well-versed in QCD to fully appreciate the answer there. I know ...
- 11.8k
2
votes
2
answers
573
views
Understanding the prefactor $\frac{\theta g^2}{32\pi^2}$ of the $F\tilde{F}$ term in Yang-Mills theories
The most general Yang-Mills (YM) action consistent with Lorentz invariance, gauge invariance and renormalizability should contain a term $$\kappa F_{\mu\nu a}\tilde{F}^{\mu\nu a}\tag{1}$$ where $\...
- 26.8k
1
vote
2
answers
746
views
How does the underlying symmetry of QCD imply the allowance of a 4-gluon vertex?
Quantum chromodynamics allows for a four-gluon vertex such as this, in a diagram
Such a vertex would never be allowed in quantum electrodynamics, which has an underlying U(1) gauge symmetry.
I know ...
- 324
2
votes
0
answers
72
views
What happens to large gauge transformations in gauges different from the temporal gauge?
There are already several questions regarding the meaning and definition of large gauge transformations.
Discussions of large gauge transformations typically only happen in the context of the ...
- 10.1k
0
votes
0
answers
203
views
QCD vs. QED gauge invariance
Trying to understand the difference between QED and QCD gauge invariance treatment I found the following paper: https://arxiv.org/abs/1101.3425
I have the following questions:
I understand Eq. (42) ...
- 1,597
4
votes
0
answers
143
views
What is the relation between the Gribov problem and color confinement?
I have heard that the Gribov problem is in some way related to color confinement (For instance: Gribov copies and confinement). Although I understand what both the Gribov and confinement problems are, ...
- 17.8k
3
votes
1
answer
267
views
Isn't there a unique vacuum of the Yang-Mills quantum theory?
The theta vacua$^1$ of a Yang-Mills quantum theory are given by $$|\theta\rangle=\sum\limits_{n=-\infty}^{\infty}e^{in\theta}|n\rangle.$$ In Srednicki's Quantum Field Theory, he claims that the ...
- 26.8k