All Questions
Tagged with quantum-chromodynamics yang-mills
22
questions
22
votes
1
answer
7k
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 ...
- 532
35
votes
2
answers
5k
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 ...
- 5,569
6
votes
1
answer
2k
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 ...
- 26.8k
2
votes
2
answers
696
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?
- 253
16
votes
1
answer
2k
views
Are "confinement" and "asymptotic freedom" two sides of the same coin?
On Wikipedia it says that the two peculiar properties of quantum chromodynamics (QCD) are: confinement and asymptotic freedom.
Asymptotic freedom is the idea that at low energies we cannot use ...
- 5,228
5
votes
2
answers
530
views
What is relevant for Yang-Mills theory below $d = 4$?
There are two ways to write the Lagrangian for Yang-Mills, differing by the scaling of the Yang-Mills field. Fancy theorists tend to write
$$S = \int d^dx \, \frac{1}{4e^2} \, \text{tr}(F^2)$$
while ...
- 103k
4
votes
1
answer
2k
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,...
- 1,154
4
votes
1
answer
547
views
Glueball mass in non-abelian Yang Mills theory
How can the glueball mass be calculated in Yang-Mills theory?
- 327
3
votes
2
answers
2k
views
What are chromoelectric and chromomagnetic fields?
Are they the normal electric and magnetic fields from Maxwell fields? Or are they just the corresponding components from $G_{\mu\nu}^a$ (the gluon fields), say chromoelectric fields are simply $G_{0i}^...
- 3,691
10
votes
1
answer
888
views
Why is is the vacuum expectation value (VEV) of the axion field such that it cancels the theta angle of QCD?
Why does the vacuum expectation value of the axion field $a(x)$ take on the value $\langle a \rangle = -\theta f_a/\xi \sim -\theta$, i.e. the vacuum theta angle of QCD? (Sources or proof if possible.)...
- 101
8
votes
1
answer
387
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.
...
- 4,619
7
votes
1
answer
2k
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 ...
- 4,561
6
votes
2
answers
2k
views
double line notation (three and four gluon vertices) - how is this a simplification?
This is closely related to my previous post Double line notation - gluon propagator
I'm trying to understand the double-line vertices for the gluon in the case of a $U(N)$ gauge group. Normally, the ...
- 3,719
6
votes
1
answer
591
views
Colour decomposition of $n-$gluon tree amplitude
I have here a $SU(N_c)$ Yang-Mill's theory and let the index $i$, label the $n$-gluons, and $\{k_i, \lambda_i, a_i\}$ be its momenta, helicity and colour index and $\cal{A}_n^{tree/1-loop}(\{k_i, \...
- 4,561
5
votes
0
answers
428
views
Unitarity of the S-matrix and Feynman Diagrams
There are several questions on the unitarity of the S matrix, but unfortunately non of them answers directly the following question.
The S matrix is unitary and that can be proven by the fact that ...
- 1,210