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In physics, Fermi's interaction is an old explanation of the weak force, proposed by Enrico Fermi. Four fermions directly interact with one another. For example, this interaction is directly able to split a neutron (or a down-quark) to an electron, antineutrino and a proton (or an up-quark).

Tree Feynman diagrams describe the interaction remarkably well. Unfortunately, loop diagrams cannot be calculated reliably because Fermi's interaction is not renormalizable. The solution is to replace the four-fermion contact interaction by a more complete theory (see UV completion) — an exchange of a W boson or a Z boson as explained in the electroweak theory. The electroweak theory is renormalizable.

Before the electroweak theory and the Standard Model were constructed, George Sudarshan and Robert Marshak, and also independently Richard Feynman and Murray Gell-Mann were able to determine the correct tensor structure (vector minus axial vector, V−A) of the four-fermion interaction.

The strength of Fermi's interaction is given by a "Fermi constant" <math>G_F</math>. In modern terms,

<math>G_F = {\sqrt{2} \over 8} {g^2 \over m_W^2}</math>

where <math>g</math> is weak coupling constant and <math>m_W</math> is the mass of W boson.

<math>G_F = 1.16639(1) x 10^{-5} GeV^{-2}</math>

See four-fermi interaction

Four-fermion interactions
Fermi's theory Thirring model Gross-Neveu model Nambu-Jona-Lasinio model BCS theory Hubbard model Luttinger liquid

pl:Teoria Fermiego