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.

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. They obey Fermi-Dirac statistics and come in 3 main categories:

  • Weyl Fermions (Massless)
  • Dirac Fermions (Massive)
  • Majorana (Self-Antiparticle)

In supersymmetric theories, spin-3/2 particles exist.

Further Classification

The known fermions divide further those that interact via the strong interaction (hadrons and quarks) and those that do not (leptons).

Hadrons include the proton and neutron as well as mesons such as pions and kaons.

Leptons come in three (known) generations each including a charged species (electrons, muons, and taus) and an uncharged species (the corresponding neutrinos).

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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 procedure of integrating out the fermion fields…
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How to put spin-1/2 Fermi sea into real space representation?

For $N$ spin-1/2 free fermions, the ground state is given by the Fermi sea, $$|{\rm FS}\rangle = \prod_{|{\bf k}|
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Fermi Hubbard model in Majorana representation

I found the Fermi Hubbard model Hamiltonian given in terms of creation and annihilation operators. But it consists of spins as well. So I am not sure how to convert to Majorana representation. Is there a possibility?
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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_{}\sum_{\sigma}c^{\dagger}_{i\sigma}c_{j\sigma}, \end{equation} in which $i$ and $j$ are nearest neighbor site…
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$E=mc^2$ and particles

This is a simple question. Does the Energy create both Fermion and Boson particles ? or just only the Fermion particles?
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why is photoelectric effect independent of temperature

what is the connection between the fact that the free electrons in a metal body obey fermi statistics law and that the photoelectric effect is virtually temperature independent?