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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Can bosons that are composed of several fermions occupy the same state?

It is generally assumed that there is no limit on how many bosons are allowed to occupy the same quantum mechanical state. However, almost every boson encountered in every-day physics is not a fundamental particle (with the photon being the most…
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Does black hole formation contradict the Pauli exclusion principle?

A star's collapse can be halted by the degeneracy pressure of electrons or neutrons due to the Pauli exclusion principle. In extreme relativistic conditions, a star will continue to collapse regardless of the degeneracy pressure to form a black…
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Why fermions have a first order (Dirac) equation and bosons a second order one?

Is there a deep reason for a fermion to have a first order equation in the derivative while the bosons have a second order one? Does this imply deep theoretical differences (like space phase dimesion etc)? I understand that for a fermion, with half…
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What's the point of Pauli's Exclusion Principle if time and space are continuous?

What does the Pauli Exclusion Principle mean if time and space are continuous? Assuming time and space are continuous, identical quantum states seem impossible even without the principle. I guess saying something like: the closer the states are the…
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"Velvet way" to Grassmann numbers

In my opinion, the Grassmann number "apparatus" is one of the least intuitive things in modern physics. I remember that it took a lot of effort when I was studying this. The problem was not in the algebraic manipulations themselves -- it was rather…
Kostya
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Why do or don't neutrinos have antiparticles?

This was inspired by this question. According to Wikipedia, a Majorana neutrino must be its own antiparticle, while a Dirac neutrino cannot be its own antiparticle. Why is this true?
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Grassmann paradox weirdness

I'm running into an annoying problem I am unable to resolve, although a friend has given me some guidance as to how the resolution might come about. Hopefully someone on here knows the answer. It is known that a superfunction (as a function of…
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$\phi^4$ theory kinks as fermions?

In 1+1 dimensions there is duality between models of fermions and bosons called bosonization (or fermionization). For instance the sine-Gordon theory $$\mathcal{L}= \frac{1}{2}\partial_\mu \phi \partial^\mu \phi + \frac{\alpha}{\beta^2}\cos \beta…
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Huge confusion with Fermions and Bosons and how they relate to total spin of atom

I am supremely confused when something has spin or when it does not. For example, atomic Hydrogen has 4 fermions, three quarks to make a proton, and 1 electron. There is an even number of fermions, and each fermion has a 1/2 spin. Since there are an…
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A reading list to build up to the spin statistics theorem

Wikipedia's article on the spin-statistics theorem sums it up thusly: In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin of a particle is its intrinsic angular momentum…
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Classical Fermion and Grassmann number

In the theory of relativistic wave equations, we derive the Dirac equation and Klein-Gordon equation by using representation theory of Poincare algebra. For example, in this paper http://arxiv.org/abs/0809.4942 the Dirac equation in momentum space…
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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, and pick up a phase of -1 when rotated by 2$\pi$…
Rococo
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What is the fundamental reason of the fermion doubling?

Recall that the fermion doubling is the problem in taking the $a \to 0$ limit of a naively discretized fermionic theory (defined on a lattice with lattice spacing $a$). After such a limit one finds themselves with an additional amount (precisely…
Marek
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What carries the information for the Pauli exclusion principle to occur?

I have been reading about the exclusion principle a little bit, but I have some questions about it. How does the information about the state of electrons get "passed around" so that other electrons in similar state can not have that same state? Is…
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Why is every electron in the universe not entangled with every other electron?

According to the principles of identical particles, the wavefunction of a collection of fermions must be antisymmetric and such a state is entangled. Doesn't this mean that any given electron in the universe (which is a giant system) is entangled…
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