All Questions
18
questions
0
votes
0
answers
31
views
How to derive Fermion Propagator for Special Kinetic Term?
I am currently working through chapter 75 of the book on QFT by Srednicki. There, he considers the example of a single left-handed Weyl field $\psi$ in a $U(1)$ gauge theory. The Lagrangian, written ...
0
votes
0
answers
35
views
Left-handed fermion oscillating into right-handed fermion
Given a Dirac fermion $\psi$
$$\mathcal{L} = \bar{\psi} \gamma^\mu \partial_\mu \psi - m \bar{\psi}\psi \ ,$$
which can be written in terms of chiral left and right handed fields as
$$\mathcal{L} = \...
- 780
5
votes
1
answer
439
views
Dirac Lagrangian in Classical Field Theory with Grassmann numbers
The concept of the Grassmann number makes me confused.
It is used to describe fermionic fields, especially path integral quantization.
Also, it is used to deal with the classical field theory of ...
- 79
1
vote
0
answers
68
views
Find the fermion mass by looking at the Lagrangian
We have a Lagrangian of the form:
$$\mathcal{L} = \overline{\psi} i \gamma_{\mu} \partial^{\mu} \psi - g \left( \overline{\psi}_L \psi_R \phi + \overline{\psi}_R \psi_L \phi^* \right) + \mathcal{L}_{\...
- 980
1
vote
2
answers
188
views
Massless QED modified Lagrangian
Consider a massless theory of QED, with Lagrangian
$$\mathcal{L}_{QED}=
-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\bar{\Psi}i\gamma^{\mu}\partial_{\mu}\Psi+
e\bar{\Psi}\gamma^{\mu}A_{\mu}\Psi$$
Is there any ...
- 3,992
2
votes
2
answers
426
views
External momenta in renormalizing pseudoscalar Yukawa theory
This is a follow-up question to my earlier post here:
Now suppose we have the pseudoscalar Yukawa Lagrangian:
$$
L = \frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2+\bar\psi(i\not\...
- 1,783
3
votes
1
answer
178
views
What Object is the Dirac Lagrangian in the functional treatment of QFT, where $\Psi$ and $\bar{\Psi}$ are Grassmann-numbers?
As far as I understood, in the path integral formulation of QFT, a field configuration is modelled by a mapping
$$
x \rightarrow \Psi(x)
$$
Where $\Psi(x)$ are 4 components, each represented by 4 ...
- 6,763
1
vote
0
answers
49
views
Why does S-V or T-A couplings in Fermi weak interaction model produce electron oscillations?
In Fermi interaction model, vector bilinears were originally included in the interaction Lagrangian but since these couldn't explain nuclear spin changes other combinations were considered. However V-...
- 1,088
1
vote
0
answers
362
views
1-loop 4-point Feynman diagrams of four-fermion interactions
Consider the Lagrangian
$$\mathcal L = \bar\psi(i\gamma^\mu \partial_\mu -\sigma)\psi +\frac{c}{2}\bar\psi\psi\bar\psi\psi.$$
I would like to calculate the $4$-point fermion interaction amplitude to ...
- 1,215
1
vote
0
answers
54
views
Mass term in QCD is not hermitian? [duplicate]
Accordingly to the result
$$
(\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
1
vote
0
answers
426
views
A proof that Heisenberg's and Euler Lagrange's equations are equivalent in QFT [closed]
I asked this before (link, link) but I think people didn't understand what I was asking, so I am going to try again . Thanks for everyone that helped so far.
In QFT, Heisenberg's equation is ...
- 267
1
vote
1
answer
272
views
Correction to the fermion propagator
Given the Lagrangian
$$\mathscr{L}=\bar{\psi}\left(i\partial\!\!\!/-m\right)\psi
+\frac{1}{2}\left(\partial\phi\right)^2- \frac{1}{2}M^2\phi^2 - g\bar{\psi}\psi\phi^2,$$ calculate the propagator ...
- 205
2
votes
1
answer
1k
views
Fermion-Fermion scattering in Yukawa theory
The interaction term in the Lagrangian for Yukawa theory is given by
$$
\mathcal{L}_\text{int} = -g\phi\bar{\Psi}\Psi,
$$
where $g$ is the coupling constant, $\phi$ some scalar field and $\Psi$ a ...
- 723
3
votes
1
answer
490
views
Connection between "classical" Grassmann variables and Heisenberg Equation of motion
I have been reading di Francesco et al's textbook on Conformal Field theory, and am confused by a particular statement they make on pg 22.
Let $\{\psi_i\}$ be a set of Grassmann variables. Starting ...
- 2,949
-1
votes
2
answers
315
views
Fermion Lagrangian with linear momentum versus quadratic momentum
$$
L = \bar{\psi} (\gamma^\mu (p_\mu -A_\mu)- m)\psi
\tag{1}
$$
$$
L = \bar{\psi} ((\gamma^\mu( p_\mu-A_\mu))^2 - m^2)\psi
\tag{2}
$$
Is there a difference between the two Lagragians in equations 1 ...
- 2,107