All Questions
40
questions
0
votes
0
answers
73
views
Questions about fundamental solutions and propagators for the Dirac operator
I thought that propagator is a synonym for fundamental solution. But that seems not to be the case since in this answer it is said that an expression with delta function on a surface has to be ...
- 101
1
vote
1
answer
92
views
Non-Hermiticity of the Dirac Hamiltonian in curved spacetime
In flat spacetime, Dirac fermions are classically described by the action
$$
S=\int d^Dx\;\bar\psi(x)\left(i\gamma^a\partial_a-m\right)\psi(x).
$$
One can generalize this to a general curved spacetime ...
- 503
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
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 $$ \psi(x) = \int \frac{d^3p}{(2\pi)^3} \frac{1}{2E_P} \sum_{r=1}^{2} \left( a_p^r u^r(p) ...
1
vote
0
answers
67
views
Deriving Euler-Lagrange Equations in Light-Front Quantization from the Heisenberg Equation
I'm delving into light-front quantization, with a focus on understanding the roles of good and bad fermions. Using Collins' formulation in Foundations of Perturbative QCD, we define the projectors as:
...
- 11
0
votes
1
answer
171
views
How to compute the amplitude of a Feynman diagram with a loop containing a fermion and a scalar?
I know that when we have a Feynman diagram with a fermion loop, we must take the trace and, by doing so, we get rid of the $\gamma$ matrices.
What if we have a diagram like the one in the picture ...
- 313
1
vote
0
answers
60
views
Diverging integral in massive fermionic field correlator
I'd like to understand the concept of the 2-particle quantum correlator for massive fermions with mass $m>0$ in 1 spatial dimension: $$C(x,y)=\langle 0|\psi(x)\psi^{\dagger}(y)|0\rangle=\int_{-\...
- 11
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
$$\begin{align}
\langle 0|\bar\psi(y)_b\psi(x)_a|0\rangle = (\gamma \cdot p -m)_{ab}\int\frac{d^3p}{(2\pi)^3}\frac{1}{2E_p}Be^{ip(x-y)}\...
- 169
3
votes
2
answers
239
views
Connection between column matrix and Grassmann numbers in Dirac field
In canonical quantization the Dirac equation is a complex column matrix, while in path integral formulation it's Grassmann numbers.
Is there a formula to convert from complex matrix to Grassmann ...
- 925
0
votes
1
answer
365
views
Chiral symmetry of the Euclidean action for fermions
In the literature, such as QFT Volume-II by Weinberg, p.368, the chiral anomaly is derived using Euclidean path integral. To formulate the question, let's start with the Minkowski space with signature ...
1
vote
0
answers
103
views
Why is the anticommutation relation for the Dirac field between fields? [duplicate]
The commutation relation for neutral Klein Gordan field is
$$[\phi(x,t),\pi(x',t)]=i\delta^3(x-x')$$
with all other commutators zero;
The commutation relation for charged Klein Gordan field is
$$[\phi(...
- 789
1
vote
1
answer
224
views
Geometric Quantization of Dirac spinor in QFT
I have been using resources such as, Geometric quantization, Baykara Uchicago, to get a deeper insight into geometric quantization. However, it seems to me that this theory is only valid for quantum ...
- 408
2
votes
0
answers
113
views
Coherent state path integral for Dirac fermions
I’m trying to derive the fermionic path integral for the Dirac theory using the coherent state path integral, but I’m not able to get around the presence of a $\gamma_0$ making it look different from ...
- 968
0
votes
0
answers
57
views
Classifying elementary fermions
Familiar elementary (non-composite) relativistic fermions are of the Dirac, Weyl, and Majorana kinds. Are there other kinds allowed in principle by relativistic quantum physics? If not, why not?
Are ...
- 11