Dirac adjoint

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The Dirac adjoint <math> \bar\psi <math> of a spinor field <math>\ \psi <math> is defined to be the spinor field <math>\ \psi^{\dagger} \gamma_0 <math>, where <math>\ \gamma_0 <math> denotes the time-like Dirac matrix.

Using the Dirac adjoint, the probability density for a spin-1/2 particle field can be written as

<math> \rho = \bar\psi \psi<math>

See also: Dirac equation.