All Questions
Tagged with quantum-field-theory fermions
398
questions
1
vote
1
answer
51
views
What happens to the fermion spin when I move around it in a full circle
I would like to understand the actual meaning of the description of a fermion as a spinor. I have a background in QFT and understand the calculations, but there is a leap to the actual experiment ...
- 1,734
0
votes
1
answer
61
views
$2\pi$-rotation of fermionic states vs. fermionic operators
Given a fermionic state $|\Psi\rangle$, a $2\pi$ rotation should transform it as
\begin{equation}
|\Psi\rangle \quad\to\quad -|\Psi\rangle \,,
\end{equation}
On the other hand, given a fermionic ...
- 393
0
votes
0
answers
69
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
3
votes
0
answers
48
views
Field strength renormalization for fermions
Following section 7.1 and 7.2 in Peskin and Schroeder (P&S), I've tried to consider what the derivation of the LSZ formula looks like for (spin $1/2$) fermions (in the text, they explicitly ...
- 823
3
votes
0
answers
74
views
Application of Callias operator in physics
In his article "Axial Anomalies and Index Theorems on Open Spaces" C.Callias shows how the index of the Callias-type operator on $R^{n}$ can be used to study properties of fermions in the ...
- 31
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31
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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 ...
1
vote
0
answers
38
views
Regarding vanishing of a triangle diagram
Furry's theorem ($C$ symmetry) is very important in calculations in QCD, Electroweak theory. Primarily it says everything about QED (three photon triangle diagram), but can be extended to QCD, and ($Z$...
- 534
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votes
1
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59
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Exact definition of topological non-identical diagrams
It is often said that Feynman diagrams for fermions do not have symmetry factors.
Consider I have a spinless fermionic quantum many-body system with Hamiltonian:
$$H=\int_{r}\psi^{\dagger}(r)\frac{\...
- 21
1
vote
1
answer
85
views
Non-Hermiticity of the Dirac Hamiltonian in curved spacetime
In flat spacetime, Dirac fermions are classically described by the action
$$
S=\int d^Dx\;\bar\psi(x)\left(i\gamma^a\partial_a-m\right)\psi(x).
$$
One can generalize this to a general curved spacetime ...
- 495
2
votes
0
answers
75
views
Different ways to understand fermions [closed]
I first learned about fermions in my atomic physics class, where the teacher said that electrons obey the Pauli exclusion principle. Later, in my quantum mechanics class, I learned about identical ...
- 368
1
vote
0
answers
41
views
Cubic coupling beyond Yukawa
Consider a massless Dirac or Majorana fermion $\psi$ and a massless scalar $\phi$. They interact through a Lagrangian $\mathcal{L}_I(\phi,\psi)$. I would like to understand what are the cubic ...
- 165
3
votes
0
answers
60
views
Fermions coupled to BF theory and asymptotic freedom
Suppose we couple $N$ colors of fermions to an $SU(N)$ gauge field $A$, but instead of a Yang-Mills action, there is a BF theory that restricts the gauge field to be flat $dA+A\wedge A\equiv F=0$ (by ...
- 8,815
2
votes
0
answers
53
views
Interpretations of wave numbers between open and periodic boundary conditions
I'm curious about the difference in physical interpretation between open and periodic boundary conditions (OBC and PBC) although they are identical in the thermodynamic limit.
For simplicity, let's ...
- 165
3
votes
2
answers
370
views
Proving a Grassmann integral identity
How to prove the following identity
$$
\begin{align}
\int {\rm d} \eta_{1} {\rm d} \bar{\eta}_{1} \exp\left(a \left(\bar{\eta}_{1}-\bar{\eta}_{0}\right)\left(\eta_{1}-\eta_{0}\right) + b \left(\bar{\...
- 680
3
votes
1
answer
99
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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 ...
