What is Fermion: Definition and 110 Discussions

In particle physics, a fermion is a particle that follows Fermi–Dirac statistics and generally has half odd integer spin: spin 1/2, spin 3/2, etc. These particles obey the Pauli exclusion principle. Fermions include all quarks and leptons, as well as all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics.
Some fermions are elementary particles, such as the electrons, and some are composite particles, such as the protons. According to the spin-statistics theorem in relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.
In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore, what is usually referred to as the spin statistics relation is in fact a spin statistics-quantum number relation.As a consequence of the Pauli exclusion principle, only one fermion can occupy a particular quantum state at a given time. If multiple fermions have the same spatial probability distribution, then at least one property of each fermion, such as its spin, must be different. Fermions are usually associated with matter, whereas bosons are generally force carrier particles, although in the current state of particle physics the distinction between the two concepts is unclear. Weakly interacting fermions can also display bosonic behavior under extreme conditions. At low temperature fermions show superfluidity for uncharged particles and superconductivity for charged particles.
Composite fermions, such as protons and neutrons, are the key building blocks of everyday matter.
The name fermion was coined by English theoretical physicist Paul Dirac from the surname of Italian physicist Enrico Fermi.

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  1. G

    A Problem evaluating an anticommutator in supersymmetric quantum mechanics

    I am trying to reproduce the results of a certain paper here. In particular, I'm trying to verify their eqn 5.31. The setup is N = 4 gauge quantum mechanics, obtained by the dimensional reduction of N = 1 gauge theory in 4 dimensions. ##\sigma^i## denotes the ith pauli matrix. ##\lambda_{A...
  2. phos19

    I Fermi energy for a Fermion gas with a multiplicity function ##g_n##

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  3. S

    I Propagator of massless Weyl field

    I have this Lagrangian for a free massless left Weyl spinor, so it’s just the kinetic term, that can be written embedding the field into a larger Dirac spinor and then taking the left projector in this way: $$i \bar{\psi} \cancel{\partial} P_L \psi$$ Srednicki says that the momentum space...
  4. S

    I Noether currents for a complex scalar field and a Fermion field

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  5. S

    I 1-loop Fermion mass correction in toy EFT

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  6. P

    A Weyl Fermion in an infinite well

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  7. The black vegetable

    A How to find the gamma function for a fermion vacuum energy calculation?

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  8. G

    A Fermion mass terms in Peskin and Schroeder's book

    I'm currently looking at how fermion masses are produced via the Higgs mechanism in "An Introduction to Quantum Field Theory" by Peskin and Schroeder. It all makes a lot of sense and I've been fine with it so far, but I ended up getting stuck on something that's driving me nuts. I feel silly...
  9. RicardoMP

    A Trace of a product of Dirac Matrices in a Fermion loop

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  10. Physics4Funn

    A Another question about a Causal Fermion System

    What are the specific objections to Felix Finster's Casual Fermion System besides "many objections" and "very exotic, and very, very far from mainstream"? The comment in the summary above says forget about the Dirac sea. I am sorry, but CFS is an extension of the Dirac sea idea written in...
  11. C

    A Spin change of Fermions and quantum energy spectrum

    Okay i was reading abrikosov's book and he said since in QM spin only changes by integer values boson excitiation happens one at a time and fermion ALWAYS appears or disappears in pairs. but isn't change from a spin up to spin down 1/2 to -1/2? or i had the wrong convention which |1/2| shouldve...
  12. F

    I Scattering of a scalar particle and a Fermion

    Hello everyone, I am working on the following problem: I would like to determine the invariant Matrix element of the process ##\psi\left(p,s\right)+\phi\left(k\right)\rightarrow\psi\left(p',s'\right)+\phi\left(k'\right)## within Yukawa theory, where ##\psi\left(p,s\right)## denotes a fermion...
  13. Demystifier

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  14. Jamister

    A How can infrared divergences in the fermion propagator be cured in QED?

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  15. hilbert2

    A Exploring the 2-D Ising Model & Its Continuum Limit

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  16. hideelo

    Composite Fermion Approach to FQHE

    I am following David Tong's notes on the Quantum Hall Effect (https://arxiv.org/abs/1606.06687). One of the approaches he takes to the FQHE is the composite fermion approach (Section 3.3.2). There are two things I am struggling with. First of all he says that a vortex is something around which...
  17. J

    I Some questions about electrons and the Fermi energy

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  18. YoungPhysicist

    B Can liquid helium conduct heat infinitely fast?

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  19. Spinnor

    I A Fermion interacts with the Higgs field

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  20. YoungPhysicist

    B How could a Majorana fermion exist?

    Acoording to the internet, majorana fermions are particles which its antiparticle is itself. But shouldn't particles and antiparticles annihilate each other? Then how could such particle exist or being predicted?
  21. A

    I Recovering Fermion States in New Formalism?

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  22. M

    I Commuting observables for Fermion fields?

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  23. J

    I Causal Fermion System and revival of Dirac Sea

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  24. N

    I Magnetic moment of a massless charged Fermion?

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  25. V

    I Is the Fermion number operator squared equal to itself?

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  26. L

    Need help finding fermion energies and probabilities

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  27. N

    I Eigenvalues of Fermionic field operator

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  28. S

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  29. S

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  30. S

    A Flow of charge on fermion propagator

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  31. kiwaho

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  32. Safinaz

    I Fermion Self-Energy: Calculation and Analysis

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  33. K

    I The Higgs Field and Fermion Generations: Stability and Mass

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  34. B

    B Exploring Fermion Fields: Experimental Evidence for Matter Waves and Fields

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  35. L

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  36. L

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  37. C

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  38. S

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  39. M

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  40. Finny

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  41. Ravendark

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  42. S

    Why chiral fermions don't exist in odd dimensions?

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  43. L

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  44. E

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  45. L

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  46. X

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  47. M

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  48. U

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  49. C

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