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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53 views

Interpretation of Fermi-Dirac statistics

I was reading that as temperature increases the energy at which $n(E)=0.5$ shifts to lower energies as these lower energy states become depopulated. Could someone explain that, what it means and why ...
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1answer
56 views

Is my Summary of a Spinor Bundle Associated with a String Worldsheet Correct?

I've been having difficulty finding a source that lists all the properties of the spinor bundle of a string worldsheet explicitly, so I've had a go at creating my own description. I'd really ...
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19 views

Fermion counting operator for open superstring

In Barton Zwiebach's A First Course in String Theory, in section 14.4, there's a fermion counting operator $(-1)^F$ which is supposed to give you $+1$ if the state is bosonic, or $-1$ if the state is ...
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30 views

What is the number of fermions in Kitaev honeycomb model?

One way to solve the Kitaev honeycomb model: $$ H = J_x \sum_{\textrm{x links}, <ij> } \sigma^x_i \sigma^x_j + J_y \sum_{\textrm{y links}, <ij> } \sigma^y_i \sigma^y_j + J_z ...
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45 views

Fermions in a well

I have two identical fermions in an infinite potential well. They are non-interacting. How should I show that the first excited state is four-fold degenerate? Is the wavefunction just the ...
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77 views

A problem with the loosing identity by fermions and the order of applying operators

This question comes in consequence of another one. I want to stress a problem that none of the answers addressed it. For making my problem more understandable let me first remind a well-known state, ...
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125 views

Fock Space and fermionic annihilation & creation operators

I have been trying very hard to understand, I am reading Ballentine's book on this topic, but I need help: I realized that I don't understand how many particle states work with the creation & ...
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1answer
24 views

Fermi distribution and ideal gas

I was wondering about the following: If we have ideal gas particles, then $E \ge 0$, so one would expect that the state $E=0$ is occupied with probability one for low temperatures, but this is not ...
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46 views

Where in nature does a fermionic coherent state occur?

We see evidence of bosonic coherent states everywhere. Lasers and microwave circuits naturally condense into photonic coherent states and resonators do the same except with phonons. A coherent state ...
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49 views

Multivariable functions of Grassmann numbers

I'm trying to derive the closed form of the fermionic coherent state defined by the relation: $$ f_i|\vec{\eta}\rangle = \eta_i |\vec{\eta}\rangle \tag{4.10} $$ My book (Atland and Simons, Condensed ...
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20 views

What would influence two or many photons to collide and create an electron-positron fermion pair?

If there were billions of photons around in nothing - no gravity, no electromagnetic fields, etc., what (if anything) would cause the photons to interact in a way that would cause a collision ...
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47 views

Ladder operators evolution for fermions

For the free Dirac field we have $$ \psi(x) = \sum_s\int d\Omega_{m}\frac{1}{\sqrt{2}k_0}\left(b(\mathbf{k},s)u(\mathbf{k},s)e^{-ik\cdot x}+d^\dagger(\mathbf{k},s)v(\mathbf{k},s)e^{+ik\cdot ...
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62 views

Stress-energy tensor for a fermionic Lagrangian in curved spacetime - which one appears in the EFE?

So, suppose I have an action of the type: $$ S =\int \text{d}^4 x\sqrt{-g}( \frac{i}{2} (\bar{\psi} \gamma_\mu \nabla^\mu\psi - \nabla^\mu\bar{\psi} \gamma_\mu \psi) +\alpha \bar{\psi} \gamma_\mu ...
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50 views

How to deal with coupled fermion boson operators?

I am a beginner in field theory and I have an exercise where I have a product of coupled fermion boson operators? $$ \hat{b_{l} }^{\dagger}\hat{c_{l^{'}} }^{\dagger}\hat{a_{q} }\hat{b_{l} ...
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62 views

Charge operator for Dirac spinor

In QED, the gauge transformation which acts upon a fermionic field $\psi$ is $$\psi'(x)= e^{i \alpha(x) Q}\psi(x)$$ where $Q$ is the charge operator. Most of the time it's just written as $$\psi'(x)= ...
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1answer
38 views

Density depletion for Fermions

In my recent advanced statistical physics class, I read about the density depletion of Fermions, which are "defending" a given volume around them against other Fermions, while the exchange hole ...
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1answer
29 views

Can a Fermi gas and a Bose gas be both at the same pressure and temperature?

The title says it all: can a Fermi gas and a Bose gas be both at the same pressure and temperature? It comes from a quiz about statistical mechanics
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40 views

In which part of physics can we utilize the rotational antisymmetry of certain wave functions?

Just a quick question - I fail at Googling this topic since I do not remember clearly, in which case (e.g. for what type of particles) is the wave function antisymmetric in terms of spatial rotation ...
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77 views

Helium Nucleus as boson

I am rather perplexed with this fact that though Helium Nucleus is a boson, the particles insides it: protons and neutrons are essentially fermions. How the nucleus which is made by fermions can be a ...
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1answer
39 views

Fermions and Bosons

For fermions $$P-\frac{Nk_BT}{V}\geq 0 $$ and for bosons, $$P-\frac{Nk_BT}{V}\leq 0$$ What can we understand from these results.
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61 views

Supersymmetry transformations as coordinate transformations

Usually, a supersymmetry transformation is carried out on bosonic and fermionic fields which are functions of the coordinates (or on a superfield which is a function of real and fermionic ...
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1answer
30 views

Derivation of Fermi level for T>0

I am working through the derivation of the Fermi level $ \mu_0$ for T>0. However, at one point in the notes I have, it states without any explanation that: $$ \int_0^\infty F'(\epsilon) ...
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2answers
54 views

Why don't we have particles whose wavefunctions are symmetric wrt one exchange operator and anti-symmetric wrt other exchange operator?

Consider a system with $n$ identical particles. Let the wavefunction of the system be $\psi(r_1,\ldots, r_2)$. Let $P_{a,b}$ represent the exchange operator which exchanges particle $a$ with particle ...
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1answer
28 views

does electron - positron pair annihilation occur when E is negative?

Suppose I release an electron-positron pair from rest at a distance of $r$. Then the particles attract each other and collide. The total energy $E$ is $$E = 2m_ec^2-\frac{e^2}{4\pi\varepsilon_0r},$$ ...
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215 views

Are all fermions massless at high temperatures?

According to the standard model, the electroweak symmetry is unbroken at high temperatures, and therefore all gauge bosons are massless then. But since fermions are said to acquire mass by a different ...
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727 views

Is deuterium a boson or a fermion?

I want to know if deuterium is a fermion or boson. Please give me a descriptive answer. I tried the formula that is the combination of protons and electrons which gives odd number but the answer is ...
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4answers
793 views

What is the Difference between a Lepton and a Fermion?

As the Title Says: I am Wondering what the Difference between a Lepton and A Fermion is. I know they both have an ½ integer spin number e.g. a electron, an atom with an odd mass number such as ...
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1answer
62 views

How to calculate the speed of electrons in a metal

According to the Sommerfeld model, the electrons on the Fermi level has the relation $$ \epsilon_F=\frac{\hbar^2k_F^2}{2m_e}=\frac{1}{2}m_ev_F^2 $$ i.e. $\hbar k_F=m_ev_F$ with $k_F=(3\pi^2n)^{1/3}$ ...
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62 views

Transposition of spinors

Suppose we have two 4-components Dirac spinors, that is two non commuting objects, $\psi$ and $\chi$. We know that: $ \bar{\psi} \chi= - \chi \bar{\psi} $ $ \bar{\psi} = \psi^{+} \gamma_0 $ $+=T*$ ...
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1answer
37 views

The one-loop contribution to a time ordered product of conserved currents

In two dimensions one can define for a Lagrangian describing free Dirac fermions with $N$ associated flavours by $$\mathcal{L}=i\bar{\psi}_i\gamma^\mu \partial_\mu \psi^i $$ and associate vector ...
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1answer
65 views

Normal ordering for a two fermion case

I am trying to understand how normal ordering works. I am considering a system of two photons, with $\hat{f}_i$ and $\hat{f}_i^\dagger$ being the annihilation and creation operators, respectively. I ...
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205 views

Why doesn't this multiplication of Grassmann variables give the expected result?

Would anyone be able to tell me how srednicki goes from step $(44.29)$ to $(44.30)$? Here is the paragraph: Now let us introduce the notion of complex Grassmann variables via $$\begin{align} ...
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60 views

What is really interacting in weak interactions?

Only particles with chirality $-1$ do interact weakly. The corresponding eigenstate in the Dirac basis is $ \Psi_L = \begin{pmatrix}f \\ -f \end{pmatrix} = \begin{pmatrix}u_r {\mathrm{e}}^{-imt} \\ ...
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35 views

Minimization of a quaradic-like expression when calculating the generating functional for free Dirac field

The generating functional for a free Dirac field is $$Z_0[\eta,\bar{\eta}]=\int D\bar{\psi}D\psi \mathrm{exp}\{i\int [\bar{\psi}(x)S^{-1}\psi(x)+\bar{\eta}(x)\psi(x)+\bar{\psi}(x)\eta(x)]dx\}$$ where ...
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Are the left-chiral and right-chiral yukawa couplings equal?

I guess another way to ask this is: Does the "physical electron" spend EQUAL time being a left-chiral and right-chiral fermion, on average? Clarification: The electron switches between (-1/2 T3, -1Y) ...
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76 views

Geometric interpretation of Grassmann variable

Grassmann variables were introduced to make path-integral formalism easier to handle fermionic (anti-commutating) fields. Mathematically they represent the exterior algebra of forms (or exterior ...
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1answer
62 views

Few particle fermion system wavefuction

Suppose I have 3 fermions($\left|\psi_1\right\rangle$, $\left|\psi_2\right\rangle$, $\left|\psi_3\right\rangle$) and a system with 3 states ( $\left|1\right\rangle$, $\left|2\right\rangle$, ...
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151 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 ...
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67 views

Diffeomorphisms and the Dirac action

I have a question concerning fermions in curved space-time. Please read it to the end before suggesting the spin-connection and vierbein-based approach. I heard that there is a special way of ...
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0answers
28 views

Mean-field approach to quantum phase transitions in Fermi systems

I have a basic confusion concerning the mean-field theory of quantum phase transitions in Fermi systems. Consider as an example the BCS theory of superconductivity in a Dirac fermion system, ...
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2answers
201 views

Grassmann number representation for fermions

How one can simultaneously represent fermionic operators and its corresponding Grassmann variables, so that all the anticommutation relations between them and also states would take place? $$ ...
8
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1answer
129 views

What causes Paulis Exclusion Principle?

Currently I'm taking an astrophysics class and has now come across electron degeneracy. As far as I understand, the reason why white dwarfs and such, does not collapse, is due to this, meaning that ...
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0answers
41 views

Pauli's exclusion principle? [duplicate]

What is the idea behind Pauli s exclusion principle? Why should an electron or any particle having non integral spin obey this principle?
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1answer
143 views

Relative Minus signs from different Feynman Diagrams

I have a problem understanding the occurrence of a the relative minus signs between contributions, coming from different Feynman diagrams, involving fermions. A simple example is Bhabha scattering ...
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0answers
49 views

Quantum master equation

In the framework of Redfield Quantum Master Equation, the popular approach is to use a tight-binding model linear conductor for the modeling of the Fermionic bath. Does someone can refer me to more ...
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2answers
619 views

Is there a reason why the spin of particles is integer or half integer instead of 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 ...
2
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1answer
105 views

Two-Electron System

I'm reading the section "Two Electron System" in Sakurai's textbook and I'm stuck on the following reasoning: Let us now consider specifically a two-electron system. The eigenvalue of the ...
4
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1answer
276 views

What is the fundamental representation in field theory?

In field theory we associate to each Gauge theory a continuous group of local transformations (a Gauge group), and then we require\define fermion fields to be irreducible representations belonging to ...
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2answers
104 views

Is there any difference between massless Dirac fermions and Weyl fermions?

In graphene we call the low energy excitations around the Dirac point Dirac fermions, which are massless. Is this just by convention or is there any further differences between massless Dirac ...
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2answers
114 views

Why do the $1/2$ factor appear in the Majorana mass Lagrangian?

In case of Dirac neutrino there is no $1/2$ factor in the mass Lagrangian but for Majorana type neutrino there is a half factor in the mass Lagrangian.