All Questions
10
questions
4
votes
2
answers
672
views
Ghosts in QCD Lagrangian
The QCD Lagrangian is
$$
\mathcal{L}_{\text{QCD}} = -\dfrac{1}{2} \text{Tr}\, G_{\mu\nu}G^{\mu\nu} + \sum_i^{N_f} \bar{q_i} \left(i \gamma^\mu \mathcal{D}_\mu - m_i\right)\,q_i, \tag{1}
$$
where $\...
- 1,611
0
votes
0
answers
141
views
Deriving gluon propagator in axial gauge
I am currently checking my work against an answer and I understand most of it except I am having difficulty understanding the signs in a particular part. The question is as follows:
(a) Derive the ...
- 90
1
vote
1
answer
57
views
When can colour charge indices be equated?
I'm currently studying QFT and QCD for the first time and I have a question about the colour charge indices given below. I was asked the following question:
(a) Derive the Feynman rule for the 3-...
- 90
3
votes
0
answers
72
views
Renormalizability of massless Gross-Neveu theory
We have the following Lagrangian density:
$$ \mathcal{L} = \bar{\psi}_i i \gamma^\mu \partial_\mu \psi_i
+ \frac{g^2}{2} \left( \bar{\psi}_i \psi_i \right)^2 $$
which corresponds to the two-...
- 1,124
1
vote
1
answer
106
views
Generalities about propagators and its application to scalar chromodynamics
In an exercise for a course on quantum field theory, I am given the following Lagrangian:
$$
\mathcal{L} = -\frac{1}{2} G_{\mu\nu}^a G^{a\mu\nu} + 2 (D_\mu \phi^\dagger)^a(D^\mu \phi)^a - 2 m^2\phi^{\...
- 307
2
votes
0
answers
43
views
Is there a first-order formulation of CP-violating QCD?
In QCD without a CP violating $\theta$ term, (I believe) we can express the gauge kinetic Lagrangian in a first-order form with the field strength $F_{\mu\nu}$ taken to be Lagrange multipliers. Up to ...
- 395
1
vote
0
answers
54
views
Mass term in QCD is not hermitian? [duplicate]
Accordingly to the result
$$
(\bar{\psi}\psi)^\dagger = (-1)\bar{\psi}\psi
\tag1$$
coming from the fact that fields with and without bar anti-commutes, you can deduce that the QCD mass term
$$
-m\...
- 1,597
2
votes
0
answers
141
views
Is there any way to understand why a chiral rotation shifts $\theta$ besides the usual "path integral measure" computation?
I'm looking for a way to understand why a chiral rotation
$$ \Psi \to e^{i \alpha \gamma_5} \Psi $$
shifts the QCD $\theta$ parameter: $\theta \to \theta + c \alpha$. (I know that it also has an ...
- 10.1k
18
votes
1
answer
2k
views
Why is the strong CP term $ \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu}$ never considered for $SU(2)$ or $U(1)$ interactions?
The Lagrangian one would write down naively for QCD is invariant under CP, which is in agreement with all experiments.
Nevertheless, if we add the term
\begin{equation}
\theta \frac{g^2}{32 \pi^2} ...
- 1,872
6
votes
0
answers
550
views
How to understand the QED, QCD and standard model Lagrangians? [closed]
How do you read the QED, QCD and standard model Lagrangians? What do all the symbols and tensors represent? And, how can you derive them by yourselves?
- 609