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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57 views

Why can a left handed fermion transform into a right handed fermion and vice versa? [closed]

How (mathematically) can we show a left handed fermion turning into a right handed fermion?
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66 views

Kitaev honeycomb model: Ground state degeneracy

Consider the Kitaev honeycomb model: $\quad -J_x\sum_{x\; links} S_i S_{i+x}- J_y\sum_{y\; links} S_i S_{i+y}- J_z\sum_{z\; links} S_i S_{i+z}$. From Lieb's theorem, the ground state is given by, ...
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2answers
90 views

Fermion Lagrangian with linear momentum versus quadratic momentum

$$ L = \bar{\psi} (\gamma^\mu (p_\mu -A_\mu)- m)\psi \tag{1} $$ $$ L = \bar{\psi} ((\gamma^\mu( p_\mu-A_\mu))^2 - m^2)\psi \tag{2} $$ Is there a difference between the two Lagragians in equations 1 ...
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1answer
55 views

How many fermions?

Quick question: I just read in a PhD thesis that there are 48 fermions. I count 6 quarks + 3 leptons + 3 neutrinos times 2 for anti-particles = 24 fermions. Am I missing something?
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1answer
99 views

Grassmann numbers in the dual space

I'm reading the section on Grassmann numbers in QFT for the Gifted Amateur and I'm confused by something said therein: First, they define a coherent state for fermions $\rvert \eta \rangle$ as ...
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1answer
174 views

Why is the derivative of the Fermi-Dirac distribution negative?

Why the derivative of Fermi-Dirac distribution function at absolute zero temperature becomes negative of Dirac_Delta function. The Fermi-Dirac distribution function is \begin{equation} ...
3
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0answers
85 views

Why are coherent states necessary for defining the fermionic path integral?

I am following the discussion of fermionic path integrals and Grassmann variables in QFT for the Gifted Amateur (ch. 28). It defines a coherent state for fermions $\rvert \eta \rangle$ as ...
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1answer
91 views

What is the difference between Fermi level and Fermi edge?

Just as in title: What is the difference between Fermi level and Fermi edge? My friend makes some research about XPS and he encountered this term. He knows what is Fermi level, but never heard about ...
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63 views

Measuring the Dirac field

If the Dirac field $\psi(x)$ is to the electron as the Electromagnetic field is to the photon, why is it that we can measure the Electromagnetic field, whereas the Dirac field we cannot?
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1answer
73 views

What is the correct way of writing the antisymmetrized state of two identical fermions?

I am just confused: If I have 2 identical fermions, where one of them is in state A and the other one is in state b, and they are normalised and orthogonal, which statement is right: 1) ...
2
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1answer
108 views

How to find the normalization constant of Fermi-Dirac distribution function?

The Fermi-Dirac distribution function is given by $$f(E):=\dfrac{A}{{\mathrm e}^{(E-E_{F})\,/\,(k_{B}T)}+1},$$ where A is the normalization constant. When we sum over all the states, we get $1$. ...
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51 views

QFT decay rates in lower dimensions

My starting point is the decay of a Higgs particle into two fermions, with decay rate proportional to \begin{equation} \Gamma \propto g_\psi^2 N m, \end{equation} where $g_\psi$ is the coupling, $N$ ...
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3answers
95 views

Why is this proof that all $\overline{\psi}\psi\overline{\psi}\psi$ interactions are trivial incorrect?

This is a homework question for my quantum field theory class. I haven't been able to figure out the answer, and neither has anybody I asked. The homework was due two days ago. Consider a spinor ...
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1answer
119 views

Nature of the quantum degeneracy pressure

It is commonly known that it is the electron degeneracy pressure that prevents the collapse of a white dwarf into a neutron star, and it is not the electromagnetic force. However, it is also widely ...
4
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1answer
102 views

Dirac string and Nielsen–Ninomiya theorem

Nielsen–Ninomiya theorem states that in a lattice system one can not have just one chiral fermion. Fermions necessarily come in pairs of opposite chirality. I am wondering if one can "explain" this ...
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2answers
304 views

What is meant by fermionic and bosonic “modes”?

The paper The Dirac quantum automaton: a short review (pdf) starts off by stating: The starting point for the construction of space–time and the physical laws therein is an unstructured, countably ...
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0answers
61 views

Propagator for fermion fields and Feynman diagrams

I need some help concerning the interpretation of propagators and Feynman diagrams. The free fermion propagator is given by the contraction of two fields $\psi(x),\bar\psi(y)$: ...
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1answer
63 views

Derivation of Fermions anticommutation rule

How one might derive fermions anticommutation rule? For bosonic particles, there is no ordering issue, and its commutation relation could be easily derived. However, for fermion, is there any easy way ...
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4answers
488 views

Are fermions intrinsically non-local?

Background: When one studies quantum mechanics of more than one particle, one learns that all fundamental particles can be classified as either bosonic or fermionic. Fermions have a spinor structure, ...
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0answers
11 views

Numeric fermiomic creation operators and unit cell

I have to do some numerics (e.g. FFT in Maple/Octave) on a 1D fermionic chain without forces between the particles. The description says that two sites build an unit cell. What does this mean? And ...
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0answers
37 views

Grassmann variables

In lots of QFT and SUSY texts they give you the basic properties of left and right handed Weyl spinors, $\psi$ and $\bar{\chi}$. They state that the components of these objects, $\psi^a$ and ...
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2answers
68 views

Entangled electrons seem impossible

Two fermions cannot share the same quantum state. But two electrons can be entangled. Entangled electrons share the same quantum state. Thus a contradiction. Where is my error?
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1answer
88 views

Pauli's exclusion principle and square well potential [closed]

Consider an infinite square potential well with potential $$V(x)=\begin{cases} 0 & \text{if} -a<x<a\\ \infty & \text{otherwise.}\\ \end{cases}$$ The stationary state energies for a ...
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1answer
57 views

Why do bosons and fermions exist? [duplicate]

if i have two particles in states: |1> and |2> respectavly , and they are not identical then the combined state is |1>|2> , but if they are identical then the labels 1 or 2 are arbitrary and could be ...
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2answers
91 views

Confused about Slater Determinant

Consider a system of 2 identical fermions. $$\psi_{k_1,k_2}(x_1,x_2,m_1, m_2) = \langle x_1\,x_2\,m_1\,m_2\mid \psi \rangle$$ According to what I have read we can construct a state with the right ...
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28 views

quantum two particle system? [duplicate]

according to wiki if you have two different particle with state vectors |1> and |2> respectively than the state vectors of the combined system is the tensor product denoted: |1>|2> but if the two ...
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1answer
41 views

Question about Supermatrix algebra

This question is inspired from a reading of Appendix F of P. van Nieuwenhuizen, Supergravity, Phys. Rep. 68 (1981) pp. 369-374. Consider a "supermatrix" $$M = \left(\begin{array}{cc} A & B\\ C ...
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0answers
67 views

Connection between Lindhard susceptibility and Free energy

I've encoutered a few times, but I never got an explanation for it... How is the spin-dependent Lindhard function for the dynamical susceptibility of an electron gas $$ \chi_{\sigma,\sigma'} (q, ...
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1answer
96 views

Is this a good argument against time travel? [closed]

Two fermions in two different points of space cannot be made to exist in the same point of space. It follows then that two fermions in two different times cannot be made to exist in the same time. ...
3
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1answer
192 views

Why must fermions be antisymmetric? [closed]

I have read that fermions cannot exist in the same state simultaneously. I understand why indistinguishable particles with an antisymmetric superposition of states can't exist in the same state ...
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1answer
58 views

One stupid question about Dirac mass term and Grassmann numbers

Let's have Dirac mass term in lagrangian: $$ L_{M} = \bar{\Psi}\Psi $$ Lagrangian must be real-valued, i.e., its Hermitian conjugation doesn't change it. But due to Grassmann nature of spinor fields, ...
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1answer
53 views

Identical particles: Why only two possibilities?

Given two identical particles, Wikipedia says that the wavefunction of a combined system where the first particle is in state $|n_1\rangle$ and the other one is in $|n_2\rangle$ is ...
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117 views

Path integral for boson vs fermion (soft derivation + use )

I have been looking around for a soft derivation with a bit of detail for boson and fermion path integrals that I could understand. I have a passing knowledge generally of what a path integral is in ...
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1answer
149 views

No two identical fermions can have the same quantum state at once?

This is the Pauli Exclusion Principle, but I have a question about it... It states that no two identical fermions can have the same quantum state, but what about different fermions having the same ...
0
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1answer
88 views

Convert Grassmann numbers to real numbers [closed]

We know Grassmann numbers are complex numbers. Hence Grassmann integrals are also complex. How can we convert a Grassmann integral into real one, ie is there any transformation of converting complex ...
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2answers
138 views

Is there a phase transition for degenerate matter?

Does electron or neutron degenerate matter undergo a phase transition? Are there any thermodynamic quantities that are discontinuous?
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1answer
82 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 ...
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53 views

How to evaluate fermion operator in product state?

I have a question concerning the implementation of DMRG for fermion chains. Suppose I have a simple chain \begin{equation} H=t\sum_{<i,j>}\sum_{\sigma}c^{\dagger}_{i\sigma}c_{j\sigma}, ...
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1answer
70 views

Smoothness of the energy levels of a generic Hamiltonian

Let us take an Hamiltonian $H(\xi)$ which depends on a set of parameters $\xi$, and assume that the matrix elements $h_{ij}(\xi)$ of the Hamiltonian are smooth complex functions of the parameters ...
2
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1answer
75 views

Are Fermi-Dirac-statistics relevant to view the universal system of neutrinos?

Should the energy distribution of neutrinos be affected by Fermi-Dirac statistics? And if so, what would the consequences be? Could this locally cause weak interaction because of the Pauli Exclusion ...
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2answers
133 views

Massless bosons but not massless fermions?

I noticed some article on massless Weyl fermions and it got me thinking. I'm wondering if there is any explanation for why bosons (specifically gauge bosons) can be massless (photon and gluon) but we ...
2
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1answer
88 views

Minus sign in the time ordering operator

The time ordering operator is usually defined as $$\mathcal{T} \left\{A(\tau) B(\tau')\right\} := \begin{cases} A(\tau) B(\tau') & \text{if } \tau > \tau', \\ \pm B(\tau')A(\tau) & \text{if ...
4
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0answers
70 views

Correct way to define parity of two parafermions

I am checking the literature on parafermions and it seems that people define the parity of two parafermions to be $\gamma_{a}^{-1}\gamma_{b}$. Is this definition always valid? How does one come up ...
2
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2answers
153 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 ...
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1answer
35 views

Equivalent forms of four fermion operators?

In this paper a little below equation (15) it is said that the four fermion operator $$(q^{\dagger}\bar{\sigma}_{\mu}q)(u^{\dagger}\bar{\sigma}^{\mu}u)$$ where $q$ and $u$ are left chiral Weyl ...
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1answer
175 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 ...
3
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1answer
106 views

Fermionic Poisson bracket

I'd like to understand the Poisson bracket for fermions in classical field theory defined on a cylinder (with coordinates $(t,x)$, $x$ being the compact direction) and propagating on $T^n$ with ...
1
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0answers
62 views

About the definition of super Hilbert Spaces

I have founded in the literature at leas two different definition of Hilbert spaces: Definition 1: A super Hilbert space is a complex super-vector space $\mathcal{H}=\mathcal{H}_0\oplus ...
3
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1answer
166 views

Interacting fermions on a lattice

My rough understanding about lattice simulations of bosonic quantum field theories is that the partition function can be approximated by explicitly summing over a large number of field configurations, ...
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1answer
118 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 ...