All Questions
32
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
-2
votes
1
answer
68
views
What makes electric and magnetic fields in Yang-Mills theories gauge co-variant?
Specifically in QCD, why is it so?
- 33
0
votes
0
answers
47
views
How to derive the gauge invariance of Yang-Mills action with external source?
In the Faddeev-Popov procedure of path integral of
$$
Z[J] = \int [DA] e^{iS(A,J)},
\quad S(A,J)= \int d^4x [-\frac{1}{4}F^{a\mu\nu}F_{a\mu\nu} + J^{a\mu}A_{a\mu} ]
$$
we have used that $S(A,J)$ is ...
- 99
1
vote
0
answers
40
views
Why is it justified to focus on gauge transformations constant at spatial infinity in QCD instantons?
In the context of Yang-Mills theories and QCD instantons, much of the literature and conventional treatment hinges on the consideration of gauge transformations that remain constant at spatial ...
- 841
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
0
votes
0
answers
244
views
One-loop renormalization of the gauge coupling
Quoting Yuji Tachikawa, chapter 3 of "${\cal N}=2$ Supersymmetric Dynamics for Pedestrians":
Recall the one-loop renormalization of the gauge coupling in a general Lagrangian field theory $$...
user242231
3
votes
1
answer
59
views
Can I switch the convention of QCD by replacing coupling constant $g$ with $-g$?
There are two equivalent conventions in QCD that give two different definitions of the covariant derivative operator: ${D_\mu } = {\partial _\mu } - {\rm{i}}gA_\mu ^\alpha {T_\alpha }$ and ${D_\mu } = ...
- 41
0
votes
0
answers
107
views
What would the force arising from an $SU(4)$ gauge field operate like? (As in, how many charges, whether the boson would interact with the force, etc)
Heyo, i'm new to this all, and deadly curious what this would look like. If this isn't specific enough, lemme know.
3
votes
1
answer
258
views
What makes the (non-abelian) strong interaction so special that it leads to confinement?
The strong interaction has a coupling constant of $\alpha_s(91GeV)\approx 0.1$ whereas the weak interaction has a much lower coupling constant $\alpha_w \approx 10^{-6}$. Both theories are non-abelian ...
- 9,778
3
votes
0
answers
124
views
The 1-loop anomalous dimension of massless quark field for $SU(N)$ gauge theory with $n_f$ quark flavours
Considering $SU(N)$ gauge theory with $n_f$ massless quarks
I want to find the anomalous dimension to order of 1-loop of the massless quark field, that defined by: $$\gamma_q(g^{(R)})=\frac{1}{2Z_q}\...
12
votes
1
answer
1k
views
How many colors really are there in QCD?
In abelian gauge theory (electrodynamics), the matter fields transform like (please correct me if I am wrong)
$$
|\psi\rangle\rightarrow e^{in\theta(x)}|\psi\rangle\tag{1}
$$
under a gauge ...
- 133
2
votes
0
answers
68
views
Abelian theories with more than one charge
I have a question about the non-abelian character of QCD. In order to write a gauge-invariant Lagrangian, there must be a term with the strength tensor $X^{\mu\nu}_{a}X_{\mu\nu}^{a}$ where
$$
X^a_{\mu\...
1
vote
0
answers
237
views
Polyakov loops and Wilson loops as order parameters
At zero temperature, the confinement/deconfinement criterion is the area/length law of the following non-local parameter called the Wilson loop:
\begin{eqnarray}
W=\text{Tr}\exp\left(\oint_CA_idx^i\...
- 813
4
votes
1
answer
396
views
What is the matrix form of the gluon field strength tensor?
For electromagnetism, the matrix form
$$\Bbb{F}^{\mu \nu}=\begin{pmatrix} 0 & E_x/c, & E_y/c & E_z /c \\ -E_x/c & 0 & B_z & -B_y \\ -E_y /c & -B_z & 0 & B_x \\ -...
- 1,548
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 $\...
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