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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Connection between “classical” Grassmann variables and Heisenberg Equation of motion

I have been reading di Francesco et al's textbook on Conformal Field theory, and am confused by a particular statement they make on pg 22. Let $\{\psi_i\}$ be a set of Grassmann variables. Starting ...
4
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1answer
45 views

Should the complex conjugate of a derivative of a Grassmann number include a sign?

Take a real Grassmann variable, by which I mean $\theta=\theta^*$. We have $$\int d\theta~ \theta =1,\qquad \frac{\partial}{\partial\theta}\theta=1$$ If I define the conjugation of Grassmann ...
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2answers
37 views

Second Quantization: Do fermion operators on different sites HAVE to anticommute?

In second quantization, we assume we have fermion operators $a_i$ which satisfy $\{a_i,a_j\}=0$, $\{a_i,a_j^\dagger\}=\delta_{ij}$, $\{a_i^\dagger,a_j^\dagger\}=0$. Another way to say this is that $$ ...
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23 views

An integration problem involving Dirac distribution [closed]

This is an integration problem involving Dirac distribution which I can not solve. The following is the description of the problem. Define two functions as follows, \begin{eqnarray*} j(x) & = &...
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0answers
48 views

Re: Quantization of a Fermi field

Consider the quantization conditions for a complex Fermi field $\Psi=\Phi_1+i\Phi_2$: $$\{\Psi(x),\Psi(y)\}=\{\Psi^\dagger(x)\Psi^\dagger(y)\}=0,~~~~ \{\Psi^\dagger(x),\Psi(y)\}=\delta(x-y)$$ Compare ...
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1answer
117 views

Replacing fermionic operators with their Fourier transform and boundary conditions

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
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59 views

Confused about the substitution of the fermionic operators with their Fourier transform in an adiabatic Hamiltonian

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
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0answers
53 views

Why is there a state which is annihilated by two different operators with same absolute Fourier index?

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposed a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
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1answer
33 views

Reasoning behind taking the Fourier transform of the fermionic operators for a circular $1$D spin chain [closed]

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
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115 views

$\phi^4$ theory kinks as fermions?

In 1+1 dimensions there is duality between models of fermions and bosons called bosonization (or fermionization). For instance the sine-Gordon theory $$\mathcal{L}= \frac{1}{2}\partial_\mu \phi \...
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28 views

The definition of fidelity for fermion

The definition of fidelity for two mixed ensembles is $F=Tr\sqrt{\sqrt{\rho_1}\rho_2\sqrt{\rho_1}}$. Now I came across a problem in numerical calculation, Systems A,B are identical, but attached to ...
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37 views

Integrating out fermions in Weyl semimetals

This question may have some overlaps with Can I integrate out the fermion field that is not gapped? For a system which has isolated Fermi points, for example Weyl semimetal, what is the calculation ...
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1answer
22 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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0answers
56 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
96 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
51 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 $+q$ ...
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0answers
74 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
91 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
31 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 \,\bar\psi(x)...
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1answer
76 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
30 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
49 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 ...
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1answer
47 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 generally,...
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1answer
41 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
51 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?
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1answer
70 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 $B$...
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1answer
94 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 ...
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1answer
21 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 ...
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0answers
64 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 ...
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1answer
46 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
58 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
40 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, I'...
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1answer
45 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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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
37 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 ...
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4answers
249 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
72 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 hep-...
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1answer
85 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 ...
3
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1answer
39 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
47 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
26 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 (...
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1answer
40 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 $|3/...
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2answers
31 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
49 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
69 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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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
72 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 V}\...
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1answer
80 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 ...