In particle physics, fermions are a group of elementary (or fundamental) particles that are the building blocks of matter. In the Standard Model, elementary particles are classified as fermions and bosons. Fermions are usually related with matter, whereas bosons are related with fundamental forces (or radiation).
Fermions are subdivided into quarks and leptons. Quarks are fermions that couple with a class of bosons known as gluons to form composite particles such as protons and neutrons. Leptons are those fermions that do not undergo coupling with gluons. Electrons are a wellknown example of leptons.
Fermions come in pairs, and in three "generations." Everyday matter is composed of the first generation of fermions: two leptons, the electron and electronneutrino; and two quarks, called Up and Down. Fermions obey what is known as "FermiDirac statistics" and are named after Enrico Fermi.
Basic properties
In theoretical terms, one major difference between fermions and bosons is related to a property known as "spin."^{[1]} Fermions have odd halfinteger spin (1/2, 3/2, 5/2, and so forth), whereas bosons have integer spin (0, 1, 2, and so forth).^{[2]} (Here, "spin" refers to the angular momentum quantum number.) Fermions obey FermiDirac statistics, which means that when one swaps two fermions, the wavefunction of the system changes sign.
Given that each fermion has halfinteger spin, when an observer circles a fermion (or when the fermion rotates 360° about its axis), the wavefunction of the fermion changes sign. A related phenomenon is called an antisymmetric wavefunction behavior of a fermion.
As particles with halfinteger spin, fermions obey the Pauli exclusion principle: no two fermions can exist in the same quantum state at the same time. Thus, for more than one fermion to occupy the same place in space, certain properties (such as spin) of each fermion in the group must be different from the rest. The operation of the Pauli exclusion principle is used to explain the "rigidness" or "stiffness" of ordinary matter (contributing to the Young modulus of matter), and the stability of the electron shells of atoms (thus the stability of atomic matter). This principle is also responsible for the complexity of atoms (making it impossible for all atomic electrons to occupy the same energy level), thus making complex chemistry possible. In addition, this principle is said to be responsible for the pressure within degenerate matter, which largely governs the equilibrium state of white dwarfs and neutron stars.
In large systems, the difference between bosonic and fermionic statistics is apparent only at high densities, when their wave functions overlap. At low densities, both types of statistics are well approximated by MaxwellBoltzmann statistics, which is described by classical mechanics.
Elementary fermions
As noted above, elementary particles are classified as fermions and bosons, and elementary fermions are subdivided into quarks and leptons. When quarks are coupled together, they form composite fermions such as protons and neutrons. Leptons include the electron and similar, heavier particles (muon and tau) and neutrinos.
The known fermions of lefthanded helicity interact through the weak interaction, but the known righthanded fermions do not. Or, put another way, only lefthanded fermions and righthanded antifermions couple to the W boson.
Flavors of fermions
There are 24 fundamental (or elementary) types of fermions, referred to as fermionic "flavors." They consist of 12 quarks and 12 leptons, as listed below.
 12 leptons  six particles and six corresponding antiparticles
Composite fermions
In addition to elementary fermions and bosons, nonrelativistic composite particles made up of more fundamental particles bound together through a potential energy are composite fermions or bosons, depending only on the number of elementary fermions they contain:
 A composite particle containing an even number of elementary fermions is a boson. Examples:
 A composite particle containing an odd number of elementary fermions is a fermion. Examples:
The number of bosons within a composite particle made up of simple particles bound with a potential has no effect on whether the composite particle is a boson or a fermion.
In a quantum field theory, the situation is more interesting. There can be field configurations of bosons that are topologically twisted. These are coherent states that behave like particles, and they can be fermionic even if all the elementary particles are bosons. This situation was discovered by Tony Skyrme in the early 1960s, so fermions made of bosons are named Skyrmions.
Fermionic or bosonic behavior of a composite particle (or system) is seen only at large distances (compared to the size of the system). At proximity, where spatial structure begins to be important, a composite particle (or system) behaves according to its constituent makeup. For example, two atoms of helium cannot share the same space if it is comparable by size to the size of the inner structure of the helium atom itself (~10^{−10} m)—despite bosonic properties of the helium atoms. Thus, liquid helium has finite density comparable to the density of ordinary liquid matter.
Table of fermions and their properties
The following table is based in part on data gathered by the Particle Data Group.^{[3]}
Generation 1  

Fermion (lefthanded) 
Symbol  Electric charge 
Weak isospin 
Weak hypercharge 
Color charge * 
Mass **  
Electron  511 keV  
Positron  511 keV  
Electronneutrino  < 2 eV ****  
Up quark  ~ 3 MeV ***  
Up antiquark  ~ 3 MeV ***  
Down quark  ~ 6 MeV ***  
Down antiquark  ~ 6 MeV ***  
Generation 2  
Fermion (lefthanded) 
Symbol  Electric charge 
Weak isospin 
Weak hypercharge 
Color charge * 
Mass **  
Muon  106 MeV  
Antimuon  106 MeV  
Muonneutrino  < 2 eV ****  
Charm quark  ~ 1.337 GeV  
Charm antiquark  ~ 1.3 GeV  
Strange quark  ~ 100 MeV  
Strange antiquark  ~ 100 MeV  
Generation 3  
Fermion (lefthanded) 
Symbol  Electric charge 
Weak isospin 
Weak hypercharge 
Color charge * 
Mass **  
Tau lepton  1.78 GeV  
Antitau lepton  1.78 GeV  
Tauneutrino  < 2 eV ****  
Top quark  171 GeV  
Top antiquark  171 GeV  
Bottom quark  ~ 4.2 GeV  
Bottom antiquark  ~ 4.2 GeV  
Notes:

Notes
 ↑ The spinstatistics theorem identifies the resulting quantum statistics that differentiates fermions from bosons.
 ↑ Martinus Veltman, Facts and Mysteries in Elementary Particle Physics (River Edge, NJ: World Scientific, 2003, ISBN 981238149X).
 ↑ W.M. Yao et al. (Particle Data Group) (2006), Quarks J. Phys. G 33:1. Retrieved September28. 2022.
 ↑ B. Kayser (Fermilab) (Sep. 2005), Neutrino mass, mixing, and flavor change Particle Data Group. Retrieved September 28, 2022.
ReferencesISBN links support NWE through referral fees
 Cottingham, W.N., and D.A. Greenwood. An Introduction to the Standard Model of Particle Physics, 2nd ed. Cambridge, UK: Cambridge University Press, 2007. ISBN 9780521852494
 Griffiths, David J. Introduction to Elementary Particles. New York: Wiley, 1987. ISBN 0471603864
 Halzen, Francis, and Alan D. Martin. Quarks and Leptons: An Introductory Course in Modern Particle Physics. New York: Wiley, 1991 (original 1984). ISBN 0471887412
 Martin, B.R. Nuclear and Particle Physics: An Introduction. Chichester: John Wiley, 2006. ISBN 9780470025321
 Povh, Bogdan. Particles and Nuclei: An Introduction to the Physical Concepts. Berlin: SpringerVerlag, 1995. ISBN 0387594396
 Veltman, Martinus. Facts and Mysteries in Elementary Particle Physics. River Edge, NJ: World Scientific, 2003. ISBN 981238149X
External links
All links retrieved September 28, 2022.
 Spin Classification, Fermions, Bosons, BoseEinstein Condensation
 When bosons behave like fermions Physics World
 Review of Particle Physics Particle Data Group.
 Physics: Fermion Definition ThoughtCo
Particles in physics  

elementary particles  Elementary fermions: Quarks: u · d · s · c · b · t • Leptons: e · μ · τ · ν_{e} · ν_{μ} · ν_{τ} Elementary bosons: Gauge bosons: γ · g · W^{±} · Z^{0} • Ghosts 
Composite particles  Hadrons: Baryons(list)/Hyperons/Nucleons: p · n · Δ · Λ · Σ · Ξ · Ω · Ξ_{b} • Mesons(list)/Quarkonia: π · K · ρ · J/ψ · Υ Other: Atomic nucleus • Atoms • Molecules • Positronium 
Hypothetical elementary particles  Superpartners: Axino · Dilatino · Chargino · Gluino · Gravitino · Higgsino · Neutralino · Sfermion · Slepton · Squark Other: Axion · Dilaton · Goldstone boson · Graviton · Higgs boson · Tachyon · X · Y · W' · Z' 
Hypothetical composite particles  Exotic hadrons: Exotic baryons: Pentaquark • Exotic mesons: Glueball · Tetraquark Other: Mesonic molecule 
Quasiparticles  Davydov soliton · Exciton · Magnon · Phonon · Plasmon · Polariton · Polaron 
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