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 ...

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15 views

Average speed of a molecule in a fermion gas

Starting from Fermi-Dirac statistics, how can be calculated the average speed on the x-axis, $\langle v_{x} \rangle$, of a molecule in a fermion gas a $T= 0\ \mathrm K$?
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47 views

Could a photon also be a fermion? [duplicate]

Some phycisits have found photons that has a spin of 1,5. Now fermions has always a half spin and bosons like photons always with a whole spin. But if those photons really exists are they than ...
4
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1answer
90 views

Photons are self-conjugate but neutrinos may or may not: why is that?

Caution: This may be a very naive question but I find it confusing. Moreover, I believe this question is based on potential misconception. I would like it to be clarified. Although the neutrinos are ...
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1answer
45 views

Fermi energy of electron gas with electrostatic interaction

I have been given the following exam question and am unsure how I would go about solving it: Consider the case of a one-dimensional metal, consisting of a chain of $N$ positive charges $+q$ ...
1
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0answers
72 views

“Constant Fermion”

I was talking to a professor in my institution which works in Lorentz Violation of various QF theories. While we talk about a SUSY lagrangian, I asked him if we could have a fermion acquiring VEV and ...
2
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1answer
87 views

Can light be a spinor?

A recent discovery suggests that photons can have half-integer spins. This seems to contradict the well understood notion that photons are vector (1-form) fields What does this mean for the ...
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0answers
27 views

Variables in the Dirac Equation Lagrangian [duplicate]

(Warning: I'm a student of mathematics with no training in physics.) In derivations of the Dirac equation from an action principle, one encounters the action $$S= \displaystyle\int\,d^4x ...
3
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1answer
73 views

Peculiarity about a system of three electrons

Consider three (or any number bigger than 2) electrons without spatial degrees of freedom, thus the only degree of freedom is the spins. The Hilbert space is then formed by the tensor product of the ...
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1answer
25 views

Why don't degenerate gases expand from heat?

Degenerate gases are excellent conductors of heat. However, the fermions that compose the gas will not expand outwards due to heat, except in incredibly high temperatures. Why is this? Does it have ...
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0answers
41 views

Fierz identity for chiral fermions [closed]

First of all I define the convention I use. The matrices $\bar{\sigma}^\mu$ I will use are $\{ Id, \sigma^i \}$ where $\sigma^i$ are the Pauli matrices and $Id$ is the 2x2 identity matrix. I will use ...
3
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1answer
44 views

Supersymmetrizing bosonic actions at higher orders

Given only the bosonic terms of a supersymmetric action, using a knowledge of the (local) supersymmetry transformations, is there a systematic way of reconstructing the fermionic terms? More ...
2
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1answer
35 views

What experimental measurement could be used to show that a neutrino is a Majorana and not a Dirac particle?

I've just been reading something on the concept that neutrinos could be Majorana particles and not Dirac fermions. I was wondering what experimental measurement could show/prove that neutrinos are in ...
3
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1answer
49 views

What does it mean that a Cooper pair behaves as a boson but respects the obligations of fermions?

I refer to the fact that it has integer spin, but antisymmetric wavefunction. How is this possible?
5
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1answer
67 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 ...
5
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1answer
85 views

Spontaneous symmetry breaking of a spinor / vector field [duplicate]

Why does SSB deal only with scalar fields and not with fermion or vector fields? My professor told me that it's closely related to the Lorentz invariance of the theory, but I don't understand at all ...
0
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1answer
17 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
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0answers
59 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 ...
5
votes
1answer
45 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
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2answers
46 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?
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1answer
37 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
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1answer
39 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 ...
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0answers
24 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 ...
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0answers
32 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 ...
7
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4answers
240 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 ...
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0answers
19 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 ...
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1answer
68 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 ...
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1answer
79 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 ...
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1answer
38 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 ...
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0answers
45 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 ...
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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
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1answer
37 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 ...
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2answers
22 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
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1answer
44 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
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0answers
68 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 ...
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0answers
27 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, ...
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1answer
63 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
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1answer
65 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 ...
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0answers
49 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): $$ ...
4
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2answers
84 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
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0answers
70 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
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1answer
147 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
33 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
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1answer
64 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 ...
1
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0answers
103 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 ...
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0answers
23 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
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0answers
52 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
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0answers
63 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 ...
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1answer
59 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?
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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 ...
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0answers
34 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 ...