Fermion bilinear ($\bar{\psi }\Gamma \psi$)

A local expression containing two fermion fields and a matrix acting on Dirac spinor indices. The choices $\Gamma ={\gamma }^{\mu }$ and $\Gamma ={\gamma }^{\mu }{\gamma }^5$ give the Dirac current and axial current.

A fermion bilinear transforming as a Lorentz four-vector. For a single Dirac field this is the Dirac current; distinct flavours can give a charged or flavour-changing current.