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##

    I ran across the following problem : Statement: Consider a gas of ## N ## fermions and suppose that each energy level ## \varepsilon_n## has a multiplicity of ## g_n = (n+1)^2 ##. What is the Fermi energy and the average energy of this gas when ## N \rightarrow \infty## ? My attempt: The...
  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

    For a complex scalar field, the lagrangian density and the associated conserved current are given by: $$ \mathcal{L} = \partial^\mu \psi^\dagger \partial_\mu \psi -m^2 \psi^\dagger \psi $$ $$J^{\mu} = i \left[ (\partial^\mu \psi^\dagger ) \psi - (\partial^\mu \psi ) \psi^\dagger \right] $$...
  5. S

    I 1-loop Fermion mass correction in toy EFT

    Where does the ##m## in ##(3.2)## come from? It doesn’t seem to enter anywhere in Feynman rules for the given diagram
  6. P

    A Weyl Fermion in an infinite well

    Hello everyone, I have a problem with bounds states of the 1D Weyl equation. I want to solve the Dirac equation ##−i\hbar \partial _x\Psi+m(x)\sigma _z \Psi=E\Psi## with the mass ##m(x)=0,0<x<a##, ##m(x)=\infty,x<0,x>a##. ##\Psi=(\Psi_1,\Psi_2)^T## is a two component spinor. Outside the well...
  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

    I'm working out the quark loop diagram and I've drawn it as follows: where the greek letters are the Lorentz and Dirac indices for the gluon and quark respectively and the other letters are color indices. For this diagram I've written...
  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

    A Bosonization Formula and its Effects on Fermion Number

    Shankar, in the book "Quantum Field Theory and Condensed Matter", at page 328 writes the famous bosonization formula in the form $$\psi_{\pm}(x)=\frac{1}{\sqrt{2\pi\alpha}} e^{\pm i \sqrt{4\pi} \phi_{\pm}(x)}$$ and then writes: "This is not an operator identity: no combination of boson operators...
  14. Jamister

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

    Summary: how to cure infrared divergences in fermion propagator in QED? In calculating the fermion propagator in QED, we identify Ultraviolet and Infrared divergences. the Ultraviolet divergences solved by regularization, but I don't understand how to treat the Infrared divergences. Infrared...
  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

    Hello ,evreyone.I have two questions about fermi energy. 1,Can I claim that 'fermi energy ' play the role of chemical potential? 2,I have learned from thermal physics that only electrons near fermi level can conduct in metals.How can electrons behave like this? I can't figure out why only...
  18. YoungPhysicist

    B Can liquid helium conduct heat infinitely fast?

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  19. Spinnor

    I A Fermion interacts with the Higgs field

    In a blog post of Matt Strassler we are told about the top quark, "when the Higgs field is not zero, its presence, and the fact that it has a direct interaction with the top-left and the top-right, forces the top-left to convert over to a top-right, and back again. How often does this happen...
  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

    If the Higgs Field could exist with constant 246GeV across all of space. How come the Dirac Sea couldn't exist? If the Universe can easily accommodate Higgs Field.. why not Dirac Sea for all particles. Also how does the Dirac Sea of bosons work? Like W+, W-? Any idea? I was asking about the...
  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

    A Feynman rule for closed fermion loop in QED

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  29. S

    A Bar on a fermion field, arrows on fermion lines and particle-antiparticle nature of a fermion

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  30. S

    A Flow of charge on fermion propagator

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  31. kiwaho

    A Photon number needless conservation, consolidation possible?

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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

    Pressure of Fermion Gas

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  36. L

    Finding 2D Fermion Gas U/N with Temperature & Area

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  37. C

    A Time-ordering fermion operators

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  38. S

    Anticommutation relations Fermion creation and annihilation

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  39. M

    Confusion about Slater Determinants

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  40. Finny

    What are the prospects for the Causal Fermion System?

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  41. Ravendark

    Second functional derivative of fermion action

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  42. S

    Why chiral fermions don't exist in odd dimensions?

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  43. L

    For the Lagrangian of fermion masses, how do I understand?

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  44. E

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  45. L

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  46. X

    Interacting Fermion System Commutation

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  47. M

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  48. U

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  49. C

    How to evaluate a triangular fermion loop

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