# 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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### Resonance level model: Commutator

As a small part of an exercise on the resonant level model (all fermionic (field-)operators, $\Psi(\vec{x}) = \sum\limits_{\vec{k}}e^{i\vec{k}\vec{x}}c_{\vec{k}}$, $V$ is a constant, $d$ and $c$ ...
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### Diagonalizing a given Hamiltonian

The following Hamiltonian, which has to be diagonalized, is given: $H = \epsilon(f^{\dagger}_1f_1 + f_2^{\dagger}f_2)+\lambda(f_1^{\dagger}f_2^{\dagger}+f_1f_2)$ $f_i^{\dagger}$ and $f_i$ represent ...
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### Pauli's principle on two-electron system

I just have been introduced to the axiom "defining" bosons and fermions, namely (for fermions): Consider a collection of $N$ identical particles moving in $\mathbb{R}^3$ and having a (half-...
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### Why does normal-ordering ensure finiteness?

I will be using Jan von Delft's rigorous construction of bosonization/refermionization as an example, but I will try to explain my question in more general terms. Consider an (countably) infinite-dim (...
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### Electron density via bosonization/refermionization

I'm currently trying to understand the rigorous construction of bosonization/refermionization via Jan von Delft. In the constructive approach, we consider a system on a finite $L$ circle and thus in ...
1 vote
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### What is the correct way of looking at the Dirac field?

All quantum fields are operators in QFT. However, the Dirac field operator $\hat{\psi}$ has the following difference with the scalar field operator $\hat{\phi}$: For the $\hat{\psi}$, it makes sense ...
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### Partition function for the indistinguishable particles using symmetrization of states

In the derivation of the partition function for the the N particle ideal gas, the factor of $\frac{1}{N!}$ does not come naturally. We have to go for symmetrized and asymmetrized state. So, to derive ...
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### Why do we have distinct generations of fermions, rather than a continuous distribution of fermions with increasing mass? [closed]

As far as I am aware, each generation of fermion varies only in mass, thus my question is why do we have only three distinct generations of fermion, instead of a continuous mass spectrum of particles ...
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### $\mathcal{su}(3)$ irreps in the fermionic oscillator

Consider the fermionic oscillator, for $d=3$ degrees of freedom, with the Hamiltonian $$H=\frac{1}{2}\sum_{j=1}^3(a_{F_j}^{\dagger} a_{F_j}-a_{F_j} a_{F_j}^{\dagger})$$ Use fermionic annihilation and ...
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I am starting to do some work on free-fermionic models, but I am having some problems understanding some things. My professor led me know that the hamiltonian for free fermions without mass in a ...
1 vote
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### Are black hole singularities fermions? [closed]

I was just wondering. I apologize if this is a dumb question. Is it possible that the mass of a black hole is converted into quantum energy that gets distributed across the universe uniformly so that ...
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### Allowed k values for Spinless Fermi-Hubbard in 2D

Suppose we have the following Hamiltonian of spinless Fermi-Hubbard model: $\hat H = -t \displaystyle\sum_{<i,j>} (c^+_ic_{j} + h.c.)$ The Ground state of the free fermion Hamiltonian can be ...
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### SUSY vs bosonization and fermionization

(New to the concepts.) From what was known SUSY described a theory consisted of both a boson and a fermion pair as a symmetric counter part. Bosonization and Fermionization on the other hand described ...
### Making sense of negative $\mu$ in the Fermi-Dirac distribution
I'm trying to make sense of the fact that, in the Fermi-Dirac distribution, we have that the chemical potential can have any positive or negative value, that is $$-\infty<\mu<\infty$$ But at \$...