The Dirac adjoint <math> \bar\psi <math> of a Dirac spinor <math>\ \psi <math> is defined to be the dual spinor <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.