# Questions tagged [fermions]

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 identical fermions from occupying the same quantum state.

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### Density of states for fermions - Statistical Mechanics

I'm studying about the density of states $g(k)$ of fermions at the moment and its equations, but I'm confused about the following: This is an equation given in the notes for the course, where $N$ is ...
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### Does positive-definite Hamiltonian for a fermion make sense?

I have been told that positive-definite Hamiltonian for a fermion doesn't make sense. Can anyone explain why is that the case?
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### Mechanistic Explanations for Electron Degeneracy Pressure [closed]

Most explanations of electron (or any fermion) degeneracy pressure cite Pauli's exclusion principle for fermions. I believe such explanations tell us why we should believe such phenomena exist, but ...
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### Does the number of electrons in a material affect the density of states in this material?

The Fermi-Dirac distribution, given by $$f(E) = \frac{1}{1 + \exp\left(\frac{E - E_{\text{F}}}{k_{\text{B}} T}\right)}$$ ​ describes the probability that a state with energy $E$ is occupied by an ...
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### Massless QED modified Lagrangian

Consider a massless theory of QED, with Lagrangian $$\mathcal{L}_{QED}= -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\bar{\Psi}i\gamma^{\mu}\partial_{\mu}\Psi+ e\bar{\Psi}\gamma^{\mu}A_{\mu}\Psi$$ Is there any ...
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### Strange definition of the fermion number operator in Polchinski

In Polchinski's exposition of the RNS formalism for the superstring (String Theory: Volume II, chapter 10), in page 8, he mentions the worldsheet fermion number operator, which he calls $F$. He then ...
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### Can two electrons (with different quantum numbers) exist at the same place in space?

I was studying about the arrangements of orbitals in an atom and saw a simulation of the arrangement and that some area of a smaller orbital such as a 1s is contained inside a bigger orbital of 2s (a ...
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### Weyl Ordering of Fermions

Consider Fermion operators $c^\alpha$ and their canonical conjugates $b_{\alpha}$ (satisfying $\{c^\alpha,b_{\beta}\}=\delta^\alpha_\beta$). Is there a prescription for Weyl ordering the following ...
In Di Francesco's Conformal Field Theory, the propagator for the free Majorana fermion theory is given by $$\langle{\psi(z) \psi(w)}\rangle = \dfrac{1}{2\pi g} \dfrac{1}{z-w}$$ and the energy-...