All Questions
Tagged with quantum-field-theory fermions
399
questions
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:
$$
L = \frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2+\bar\psi(i\not\...
- 1,783
2
votes
1
answer
140
views
Confused with computing causality for Dirac field
In Peskin and Schroeder's QFT book, P.56 Eq.(3.95) mentions that
$$\begin{align}
\langle 0|\bar\psi(y)_b\psi(x)_a|0\rangle = (\gamma \cdot p -m)_{ab}\int\frac{d^3p}{(2\pi)^3}\frac{1}{2E_p}Be^{ip(x-y)}\...
- 169
3
votes
0
answers
144
views
Why is there a phase difference between these Feynman diagrams?
Here're some Feynman diagrams from my QFT notes:
I'm struggling with how to understand the minus signs on the right-hand side. For (1), is the minus sign arising from the antisymmetry of fermions? So ...
- 1,783
2
votes
1
answer
167
views
Jacobian functional matrix for fermionic path integral
I am revisiting Srednicki's book Chapter 77 and struggling to understand how you define the change of variables in the fermionic field integral
Srednicki defines the Jacobian functional matrix for the ...
- 143
2
votes
1
answer
184
views
Dirac field operator act on the right side of Green function
On P&S's QFT book, chapter 9.5, the book discussed how to derive two point correlation function for dirac field using generating functional.
Start with $$
Z[\bar{\eta}, \eta]=\int \mathcal{D} \bar{...
- 1,421
0
votes
0
answers
87
views
Field shift in Generating functional for the Dirac field
On P&S's QFT page 302, eq.(9.73) defined the generating functional for the Dirac field.
$$Z[\bar{\eta}, \eta]=\int \mathcal{D} \bar{\psi} \mathcal{D} \psi \exp \left[i \int d^4 x[\bar{\psi}(i \not ...
- 1,421
1
vote
0
answers
90
views
Understanding fermion doubling in lattice QFT
I'm studying Rothe's book on lattice gauge theory. For the case of a scalar field, we can use lattice discretization to find (using equations 3.18 and 3.19 on page 41)
$$\langle 0|T\phi(x)\phi(y)|0\...
- 789
4
votes
2
answers
234
views
How to show $\frac{\delta}{\delta \psi(x)}$ being a representation of the operator $\Psi(x)^{\dagger}$ for fermionic Schroedinger Functionals?
I'm following the book of Brian Hatfield, Quantum Field Theory of particles and strings, page 217, eq. 10.89 and the following.
The author is looking for a representation of the operators $\Psi(x)$ ...
- 6,763
3
votes
1
answer
169
views
By using a Hilbert space (enhanced by Grassmann Numbers), can we write down a full set of eigenstates of the fermionic field operator?
By extending the Hilbert space, using grassmann numbers instead of complex numbers, we can write down eigenstates of the fermionic annihilation operator $a$ without getting into trouble with the ...
- 6,763
1
vote
1
answer
82
views
Is the mass term of a neutral fermion zero?
[Note: my question can be a duplicate of this one, but I don't understand the answer given there.]
At various places, e.g., in the first slide of this lecture, it is argued that for a neutral fermion $...
- 353
3
votes
2
answers
239
views
Connection between column matrix and Grassmann numbers in Dirac field
In canonical quantization the Dirac equation is a complex column matrix, while in path integral formulation it's Grassmann numbers.
Is there a formula to convert from complex matrix to Grassmann ...
- 925
2
votes
0
answers
54
views
Electron fields does not anticommute at space-like points
In the end of page 804 and beginning of page 805 of Streater's paper
Outline of axiomatic relativistic quantum field theory
which can be find here https://iopscience.iop.org/article/10.1088/0034-4885/...
- 161
5
votes
1
answer
198
views
Counterterms in Renormalization of a Non-Renormalizable theory (Fermi theory with four fermions)
I am studying Renormalization but I don't understand why theories which have a coupling constant with negative dimension of mass requires more and more counterterms going up with the perturbative ...
- 770
0
votes
1
answer
365
views
Chiral symmetry of the Euclidean action for fermions
In the literature, such as QFT Volume-II by Weinberg, p.368, the chiral anomaly is derived using Euclidean path integral. To formulate the question, let's start with the Minkowski space with signature ...
2
votes
0
answers
52
views
Possible Eigenvalues of a real fermion-field at a single point -are they square root of infinity?
I want to start out with a real fermionic quantum field theory (in one dimension), with operators $\psi$ satisfying:
$$
\{\psi(x), \psi(y) \} = \delta(x-y)
$$
I know I won't find a state that's an ...
- 6,763