All Questions
Tagged with quantum-field-theory fermions
399
questions
3
votes
1
answer
104
views
Why can't we insist that the strong interactions must preserve $CP$?
I'm having some trouble wrapping my head around the strong $CP$ problem. I know that the non-trivial vacuum structure of QCD induces the topological theta term in the strong sector of the SM, which is ...
3
votes
0
answers
44
views
Multiple excitations of composite bosons?
Fundamental bosons, which are the mediators of the Standard Model interactions, are permitted to have multiple excitations with the same quantum number. Fermions, on the other hand, obey the Pauli ...
- 2,921
2
votes
1
answer
74
views
Product of spinors in Dirac field anticommutators
I am reading a "A modern introduction to quantum field theory" by Maggiore and on page 88 it shows the anticommutators of the Dirac field:
$$
\{\psi_a(\vec{x},t),\psi_{b}^{\dagger}(\vec{y},t)...
- 613
0
votes
0
answers
35
views
Left-handed fermion oscillating into right-handed fermion
Given a Dirac fermion $\psi$
$$\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
2
votes
1
answer
88
views
Why reasonable observables are made of an even number of fermion fields?
On Michele Maggiore book on QFT (page 91) is stated, out of nothing, that "observables are made of an even number of fermionic operator" and similar sentences is in Peskin book (page 56).
Is ...
- 613
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
63
views
Computational problem in Altland & Simons p.184
While try to understand functional field integral I encountered this problem on Altland & Simons page 184. The question is: Employ the free fermion field integral with action (4.43) to compute the ...
- 33
4
votes
1
answer
215
views
Why is commutation bracket used instead of anti-commutation bracket on page 61 of Peskin QFT?
Peskin&Schroeder was performing a trick where they used
$$J_za^{s\dagger}_0|0\rangle=[J_z,a^{s\dagger}_0]|0\rangle\tag{p.61}$$ and claimed that the only non-zero term in this commutator would be ...
- 838
1
vote
1
answer
139
views
Path integral expression for Dirac two-point function
On page 302 of Peskin and Schroeder they state a path integral expression for the Dirac two-point function.
$$\langle0|T\psi_a(x_1)\bar{\psi}_b(x_2)|0\rangle=\frac{\int\mathcal{D}\bar{\psi}\int\...
- 151
1
vote
0
answers
65
views
System interacting with Fermi Gas
My question denoted by a reduced dynamic for a system interacting with a reservoir.
Before asking the question, for completeness I will write in detail the statement of the problem and notation.
...
- 33
1
vote
1
answer
80
views
Path Integral Measure Transformation as $(DetU)^{-1}$
The path integral measure transforms as $D\Psi\rightarrow (DetU)^{-1}D\Psi$ for fermions, with $DetU=J$ the Jacobian.
I am referring to Peskin and Schroeder's Introduction to Quantum Field Theory, ...
- 57
1
vote
0
answers
65
views
Error in Peskin-Schroeder calculation? ("The Dirac Propagator equation (3.115) )
I was trying to calculate $$ \langle0|\bar{\psi}(y) \psi(x)|0
\rangle $$
where the wave-function operator is $$ \psi(x) = \int \frac{d^3p}{(2\pi)^3} \frac{1}{2E_P} \sum_{r=1}^{2} \left( a_p^r u^r(p) ...
1
vote
0
answers
53
views
Particle density and current in terms of Green function
Consider a non-relativistic free-fermion system. I am wondering how to calculate observables like average particle density and average current in terms of momentum-space Green functions. I know that ...
- 59
1
vote
0
answers
43
views
Calculating gauge propagator in minimally coupled, non-relativistic fermion system
For context, I am trying to derive Eq. 4.1 of $T_c$ superconductors">this paper. Consider the action
$$S[\psi^\dagger, \psi, a] = -\int d\tau \int d^2r \sum_\sigma \psi^\dagger (D_0-\mu_F-\frac{1}{...
- 59
3
votes
1
answer
155
views
Mean field and interacting Dirac QFT: channels and spinors
I am dealing with a QFT of Dirac fermions with an interaction term
$$L_I=\bar\psi\psi\bar\psi\psi=\psi^\dagger\gamma^0\psi\psi^\dagger\gamma^0\psi,$$
with $\gamma^0$ a Dirac matrix and $\psi$, $\psi^\...
- 503