Fermions are particles with an intrinsic angular momentum (i.e. spin) equal to a "half integer" number of fundamental units: $\frac{(2n+1)}{2} \hbar$ for integer $n$. Fermions are required to be in a quantum state that is globally anti-symmetric, which leads to the Pauli Exclusion Principle barring ...

learn more… | top users | synonyms

2
votes
1answer
28 views

Time ordering of Fermion operators

If $A$ and $B$ are fermion operators then the time ordering is defined as \begin{eqnarray} T(AB) = \left\{ \begin{array}{rl} AB, & \mbox{ if $B$ precedes $A$}\\ -BA, & \mbox{if $A$ precedes ...
0
votes
1answer
14 views

Connection between singlet, triplet two-electron states and the Slater determinant

I'm confused about a number of things concerning two-electron systems and spin. Here is (perhaps too much) exposition, skip to "the problem" if you want: Consider the helium atom in the simplified ...
1
vote
0answers
54 views

Is there a simple man's perspective of Pauli’s exclusion principle [closed]

I've been pondering over a questions from a while. Please forgive me if I am being too naive. We all know that because of Pauli's exclusion principle no two electrons can populate one state. This ...
2
votes
1answer
110 views

Would Hund's rules still be valid if the electron had spin 3/2?

One of my homework assignments in atomic physics was the following: Given electrons had a Spin of $S = 3/2$, what would be the number of the first 4 noble gasses (complete shells)? The obvious ...
0
votes
1answer
173 views

What is the form of the kinetic energy operator on a one-dimensional (real space) lattice? (In second quantization)

I'm trying to figure out how one would write down the Hamiltonian of a free fermion system (eventually in second quantization) on a one dimensional lattice and I'm having trouble both coming up with ...
0
votes
0answers
28 views

Energy in free Dirac equation [duplicate]

In one text after general solution of free Dirac equation, I read: for consistency in contribution to the energy both from particles and antiparticles we need anti commutator, and particle and ...
5
votes
1answer
41 views

Super conductivity and energy gap in fermionic/bosonic subspaces

I am trying to understand the phenomena of super-conductivity from a broader level. What I understand for now is that for super-conductivity to be possible in a system, a necessary requirement is that ...
2
votes
2answers
42 views

Do Weyl fermions carry electric charge?

Do Weyl fermions carry ordinary electric charge? That is, do they interact with, for instance, electrons or photons?
1
vote
0answers
31 views

Construct an effective field theory of neutrino mass

This is the problem I am trying to solve. I kinda write down the Lagrangian as $$L = \frac{1}{2}m_L \bar{v}_L^Cv_L$$ but I don't know how to continue. Can anyone help me?
0
votes
1answer
36 views

Why do the different lepton generations have different masses?

I've been reading Mark Srednicki's book on Quantum Field Theory, and toward the end (Chapter 88), he describes how the different generations of leptons acquire mass via Yukawa interactions. However, ...
1
vote
1answer
35 views

The fifth gamma matrix and fermion fields

I am aware of the various relations with Dirac spinors and chirality but how does the fifth gamma matrix $\gamma^5$ behave with fermion fields, $\psi$? Does the fifth gamma matrix have any particular ...
0
votes
0answers
21 views

What is the difference between the generation of mass for Fermions compared with Bosons in the standard model?

I've seen a few questions asking how the Higgs mechanism generates mass for particles of the standard model. However, I haven't seen any which specify the differences between Bosons and Fermions in ...
3
votes
2answers
71 views

Why don't we call the fermions in the standard model force carriers?

Maybe this is a chicken-and-egg problem, but couldn't we call all the bosons fundamental and treat the fermions as force carriers between them? EDIT: After all we never see the asymptotic states of ...
1
vote
0answers
26 views

Fermi momentum and Fermi energy

I have some confusion about the concept of fermi energy/fermi momentum. Is the fermi momentum always defined as $\sqrt{2mE_F}$ ,where $E_F$ is the fermi energy, or the fermi momentum depends, as ...
8
votes
4answers
236 views

Is there some special case where a fermion can mediate a force?

Looking at the comments of this questions Does the gravitino contribute to the gravitational interaction? and even considering that the answers here in this other question Why are all force particles ...
0
votes
1answer
78 views

Why is Fermi-Dirac type of distribution used in semiconductors?

We assume that distribution of electrons follows Fermi-Dirac distribution / statistics in semiconductor model which will help to find the concentrations of electron and holes and the relationship ...
9
votes
3answers
2k views

Is there a reason why the spin of particles is integer or half integer instead of, say, even and odd?

It seems to me that we could change all the current spin values of particles by multiplying them by two. Then we could describe Bosons as even spin particles and Fermions as odd spin particles. Is ...
0
votes
0answers
15 views

Fermion Trucation

I recently posted about truncating fermions in supergravity Lagrangians and got a good answer about how this gives a vev to the bosonic content and therefore freezes it to a stationary point of the ...
1
vote
1answer
72 views

Fermionic ladder operators [closed]

After reading Dirac's method for finding the eigen energies of a harmonic oscillator by means of ladder operators and commutation relations, I tried making some exercises on them. First I did a ...
0
votes
1answer
63 views

Ignoring fermions in string theory/supergravity

Often in string theory/supergravity, papers will say something along the lines of "we set all the fermions to zero and focus purely on the bosonic field content". See e.g. the final lines on p3 of ...
11
votes
2answers
311 views

Modeling non-quantum objects (in finance, sociology etc) using fermionic fields?

Please provide (if any) applications of fermionic field theory in non-physics macro contexts (finance, sociology etc). I see only bosonic fields being used mostly. The only (minor) application of ...
3
votes
1answer
35 views

Why does exchanging coordinates produce a phase of $\pm 1$ in an identical particle wavefunction?

Consider a system of two identical particles described by a wavefunction $\psi(x_1, x_2)$. There are two kinds of exchange operators one can define: Let $P$ be physical exchange. This operator swaps ...
0
votes
1answer
196 views

Chemical Potential as a function of Temperature

I have considered an ideal fermi gas. Then, we can obtain an expression for chemical potential as a function of Temperature. I want to understand the physical significance to it or what it really ...
0
votes
0answers
44 views

Quick clarification needed on degeneracy

I need some hints about degeneracy. So, I consider an energy level degenerate if there are two distinct wave functions at that energy. Then, let's say I have two spin1/2 fermions in a 1D box. Is ...
0
votes
0answers
25 views

Does an instanton couple equally to all flavors?

Do gravitational / electroweak / QCD / ... instantons couple equally to all fermion flavors? For example, do QCD instantons distinguish between the different quark flavors? Edit, due to comment ...
3
votes
1answer
33 views

How is the total spin of a particle actually measured?

Say I have a fermion whose total spin I do not know. I then use a stern gerlach setup to measure $S_z$. If I find +1/2, I could say that the total spin is $1/2$. But it could also be the eigenket ...
0
votes
2answers
21 views

Exchange principle in terms of states and coordinates?

I have seen the exchange principle written in two ways, one in terms of coordinates and the other in terms of states: If $\psi_{AB}(1,2)$ represents particle $A$ in state $1$ and particle $B$ in ...
2
votes
1answer
43 views

Current Status of the Monte Carlo Sign Problem

I've been reading about the Monte Carlo sign problem, and I am a little confused about its current status. Specifically, after reading this post When is the "minus sign problem" in quantum ...
3
votes
0answers
66 views

Why are spin-1/2 particles the simplest particles? [closed]

Paul Dirac, in his interview with Friedrich Hund, mentioned that it was to his surprise that his equation automatically incorporated spin. He said that he thought the simplest theory, for which he was ...
1
vote
0answers
25 views

Magnetisation of a degenerate electron gas in a weak field?

So I am looking at Landau's and Lifshitz's "Statistical Physics, Part I" chapter on degenerate fermi gases and specifically at chapter on Pauli's Mangetism or magnetism of degenerate electron gases, ...
0
votes
1answer
54 views

Chemical Potential in the canonical and grand canonical ensemble

I'm studying the ideal Fermi gas from "Statistical Mechanics", by R. K. Pathria. In particular, the following formula, which can be found on page 237: \begin{equation} \mu=\left(\frac{3N}{4 \pi g ...
0
votes
1answer
48 views

Could someone explain how antisymmetric position states and symmetric spin states work in an atom?

I'm reading Griffiths QM 2nd ed and he talks about how all fermions are antisymmetric in nature. Later he talks about how exchange forces with identical particles. He states that because fermions are ...
0
votes
0answers
48 views

Solving non scalar integrals in loop calculations

Consider the following integral that comes out of a loop calculation along with some fermionic propagators (e.g virtual one loop correction to a $p \gamma^* \rightarrow p'$ process such as in DIS): $$ ...
7
votes
1answer
108 views

Is there a soft Goldstino theorem?

For ordinary spontaneously broken symmetries, you can demonstrate relations between S-matrix elements with a soft goldstone emission and another S-matrix element without the emission. If I break ...
2
votes
2answers
149 views

Does charge conjugation affect parity?

Notice that these transformations do not alter the chirality of particles. A left-handed neutrino would be taken by charge conjugation into a left-handed antineutrino, which does not interact in ...
4
votes
2answers
80 views

Fermions, different species and (anti-)commutation rules

My question is straightforward: Do fermionic operators associated to different species commute or anticommute? Even if these operators have different quantum numbers? How can one prove this fact in a ...
4
votes
0answers
66 views

Physical interpretation of the chemical potential in Bose and Fermionic gas

I understand that both Fermions and bosons have the chemical potential $\nu <0$ when it is T>0, but still behave classically, the fermions would increase its chemical potential at T=0, whereas the ...
0
votes
1answer
145 views

Do I need to consider the spin of electrons when they are in infinite potential well

This is the problem I have And this is one of my books tell me what should I do And my question is: Do I need to consider spin in this case?(that is, I don't think the book is right...) I found ...
2
votes
1answer
31 views

Question about the expression of Witten Index

I am studying supersymmetry by myself. I do not understand the expression of Witten index, which is ${\rm Tr}(-1)^{F}$. What does it mean by writing $-1$ to the power of an operator $F$? Is this ...
1
vote
1answer
60 views

What are anticommuting spinor parameters $\zeta^\alpha$?

I'm reading Martin F.Sohnius, Introducing supersymmetry, page 82. It is the first time he introduces the anticommuting spinor parameters $\zeta^\alpha$ to calculate the supersymmetry variations of a ...
0
votes
2answers
127 views

Why $\delta F = B\epsilon$ and not $F=B \epsilon$ in supersymmetry?

We can express supersymmetric transformations as $$\delta F = B\epsilon, \tag{1} $$ $$\delta B = F\bar{\epsilon},\tag{2}$$ where $B$ and $F$ denote the bosons and fermions, respectively, in the theory ...
1
vote
0answers
97 views

Classical Fermion and Grassmann number

In the theory of relativistic wave equations, we derive the Dirac equation and Klein-Gordon equation by using representation theory of Poincare algebra. For example, in this paper ...
1
vote
0answers
21 views

Fermion decay into axions

Do you know any literature on fermion decay into an axion and a lighter fermion? I am especially interested in the dependence of the decay width on the initial fermion momentum. The momentum should ...
0
votes
0answers
51 views

inverse problem for specific heat of fermion .. has been solved?

hi given the specific heat is given by an integral equation $$ C(T)=\int_{0}^{\infty}d\nu g(\nu)\frac{u^{2}}{(e^{u\nu}+1)^{2}}\nu^{2}$$ where $ u= \frac{h}{kT}$ my question is is the following ...
0
votes
0answers
47 views

Model of the nucleus as fermi gas

I am taking an introductory course in modern physics, and am reviewing some of the exams from previous years. In our course, we studies the Fermi gas model for electrons in a metal. In one of the ...
4
votes
1answer
1k views

Fermion mass Higgs mechanism

How does a fermion, like an electron, get its mass through the Higgs-mechanism? Can someone explain me this with formulas (Lagrangian)? I know that the Yukawa interaction has something to do with ...
0
votes
1answer
55 views

Two fermions with total spin 1 antisymmetric wave function? [closed]

How can I prove, that two fermions with a total spin of 1 must have an antisymmetric wave function?
1
vote
0answers
74 views

Definition of partity in quantized Dirac Theory.

I'm studying from the book "An Introduction to Quantum Field Theory" from Michael E. Peskin and Daniel V. Schroeder, and I read the following: "The operator P should reverse momentum of a particle ...
18
votes
5answers
3k views

“Velvet way” to Grassmann numbers

In my opinion, the Grassmann number "apparatus" is one of the least intuitive things in modern physics. I remember that it took a lot of effort when I was studying this. The problem was not in the ...
1
vote
0answers
30 views

Majorana fermions and the continuum limit of the Ising model

In Paolo Moligini's Analyzing the two dimensional Ising model with conformal field theory lecture notes, it is shown at the end of chapter 3 that the Lagrangian of the continuum limit of the Ising ...