All Questions
Tagged with quantum-field-theory fermions
399
questions
-2
votes
0
answers
64
views
QED with massless fermions
Consider QED such that physical mass of fermions vanishes. Is it true that their bare mass also vanishes?
- 2,226
1
vote
1
answer
57
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
73
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 ...
- 426
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
3
votes
0
answers
50
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 ...
- 863
3
votes
0
answers
77
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
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 ...
1
vote
0
answers
40
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
0
votes
1
answer
59
views
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:
$$H=\int_{r}\psi^{\dagger}(r)\frac{\...
- 21
1
vote
1
answer
92
views
Non-Hermiticity of the Dirac Hamiltonian in curved spacetime
In flat spacetime, Dirac fermions are classically described by the action
$$
S=\int d^Dx\;\bar\psi(x)\left(i\gamma^a\partial_a-m\right)\psi(x).
$$
One can generalize this to a general curved spacetime ...
- 503
2
votes
0
answers
76
views
Different ways to understand fermions [closed]
I first learned about fermions in my atomic physics class, where the teacher said that electrons obey the Pauli exclusion principle. Later, in my quantum mechanics class, I learned about identical ...
- 368
1
vote
0
answers
42
views
Cubic coupling beyond Yukawa
Consider a massless Dirac or Majorana fermion $\psi$ and a massless scalar $\phi$. They interact through a Lagrangian $\mathcal{L}_I(\phi,\psi)$. I would like to understand what are the cubic ...
- 165
3
votes
0
answers
60
views
Fermions coupled to BF theory and asymptotic freedom
Suppose we couple $N$ colors of fermions to an $SU(N)$ gauge field $A$, but instead of a Yang-Mills action, there is a BF theory that restricts the gauge field to be flat $dA+A\wedge A\equiv F=0$ (by ...
- 8,815
2
votes
0
answers
54
views
Interpretations of wave numbers between open and periodic boundary conditions
I'm curious about the difference in physical interpretation between open and periodic boundary conditions (OBC and PBC) although they are identical in the thermodynamic limit.
For simplicity, let's ...
- 165
3
votes
2
answers
377
views
Proving a Grassmann integral identity
How to prove the following identity
$$
\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{\...
- 682
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,$$
with $\gamma^0$ a Dirac matrix and $\psi$, $\psi^\...
- 503
0
votes
0
answers
49
views
The renormalized fermionic operators do not anti-commute?
Let's say we have fermionic operators $a$ and $b$ (which anti-commute). In the context of a renormalization scheme (I am thinking specifically of Wilson's NRG, but it could be DMRG) I have a matrix $P$...
- 1,262
1
vote
0
answers
67
views
Deriving Euler-Lagrange Equations in Light-Front Quantization from the Heisenberg Equation
I'm delving into light-front quantization, with a focus on understanding the roles of good and bad fermions. Using Collins' formulation in Foundations of Perturbative QCD, we define the projectors as:
...
- 11
4
votes
1
answer
145
views
Anticommutation relations for Dirac field at non-equal times
I'm reading this paper by Alfredo Iorio and I have a doubt concerning the anticommutation relations he uses for the Dirac field.
Around eq. (2.25), he wants to find the unitary operator $U$ that ...
- 2,284
2
votes
1
answer
144
views
Schwartz's Quantum field theory (14.100)
I am reading the Schwartz's Quantum field theory, p.269~p.272 ( 14.6 Fermionic path integral ) and some question arises.
In section 14.6, Fermionic path integral, p.272, $(14.100)$, he states that
$$ ...
- 323
0
votes
1
answer
220
views
Inverse of an operator [closed]
I want to understand how to find the Inverse of an operator.
I know it involves the use of Green's function but I can't seem to figure out how.
Here is the actual problem:
On page 302 of Peskin&...
- 69
1
vote
0
answers
68
views
Find the fermion mass by looking at the Lagrangian
We have a Lagrangian of the form:
$$\mathcal{L} = \overline{\psi} i \gamma_{\mu} \partial^{\mu} \psi - g \left( \overline{\psi}_L \psi_R \phi + \overline{\psi}_R \psi_L \phi^* \right) + \mathcal{L}_{\...
- 980
2
votes
1
answer
284
views
How to derive the Fermion generating function formally from operator formalism?
The generating functionals for fermions is:
$$Z[\bar{\eta},\eta]=\int\mathcal{D}[\bar{\psi}(x)]\mathcal{D}[\psi(x)]e^{i\int d^4x
[\bar{\psi}(i\not \partial -m+i\varepsilon)\psi+\bar{\eta}\psi+\bar{\...
- 619
2
votes
1
answer
121
views
Why does fermion have the expansion with Grassmann-numbers?
I learn the chiral anomaly by Fujikawa method. The text book "Path Integrals and Quantum Anomalies, Kazuo Fujikawa", in the page 151, says that
…one can define a complete orthonormal set $\{...
- 129
-1
votes
1
answer
74
views
Mechanistic Explanations for Electron Degeneracy Pressure [closed]
Most explanations of electron (or any fermion) degeneracy pressure cite Pauli's exclusion principle for fermions. I believe such explanations tell us why we should believe such phenomena exist, but ...
- 1,073
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
0
votes
0
answers
43
views
Calculation about fermions via quantum field theory
I want to ask a specific question occurred in my current learning about neutrinos.
What I want to calculate is an amplititude:
\begin{equation}
\langle\Omega|a_{\bf k m}a_{\bf pj}a_{\bf qi}^{\dagger}...
- 1
0
votes
1
answer
172
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
34
views
Normalisation for a two fermion state
I'm trying to follow this paper (Fermion and boson beam-splitter statistics. Rodney Loudon. (1998). Phys. Rev. A 58, 4904)
However, I don't quite understand where some of his results come from.
...
- 33
1
vote
0
answers
44
views
Can the Keldysh occupation function have a zero for bosons or a pole for fermions?
In the Keldysh framework for nonequilibrium dynamics of quantum systems we learn that there are essentially two Green's functions that characterize a system: the retarded Green's function $G^R(\omega)$...
- 164
0
votes
0
answers
59
views
Product of delta functions in fermion self-energy at finite temperature
In the calculation of the fermion self-energy at finite temperature, there seems to be a term containing the product of two delta functions which when combined equal zero, however I fail to see why ...
1
vote
0
answers
81
views
Minus sign for incoming antifermions
In his Diagrammatica, The Path to Feynman Diagrams (Cambridge University Press, 1994; §4.5 "Quantum Electrodynamics", p. 88), M. Veltman reports the following Feynman rule for incoming ...
- 29
1
vote
1
answer
66
views
Anticommutator Relation of Quantized Fermionic Field and Fermi–Dirac statistics: How are these related?
I'm reading the Wikipedia article about Fermionic field and have some troubles to understand the meaning following phrase:
We impose an anticommutator relation (as opposed to a commutation relation ...
- 1,395
3
votes
1
answer
323
views
Classical fermions, where are they?
Context:
Studying the path integral formulation of QFT I stumbled upon a fairly simple statement: when doing loop expansions of a partition function:
$$Z[\eta ; \bar{\eta}] = \int [d\psi][d\bar{\psi}]...
- 1,611
4
votes
0
answers
138
views
Renormalisation of the fermionic triangle loop
I am trying to renormalise the following loop diagram in the Standard Model:
$\qquad\qquad\qquad\qquad\qquad\qquad$
Using the Feynman rules, we can write the amplitude as follows:
$$ \Gamma_f \sim - ...
- 387
4
votes
0
answers
128
views
Entanglement entropy in states with particle content
I am studying entanglement and its measurements in the context of a lattice model of the Dirac theory. The idea is that one has two bands, symmetric with respect to $E=0$, and the groundstate is ...
- 503