The Dirac adjoint [itex] \bar\psi [itex] of a Dirac spinor [itex]\ \psi [itex] is defined to be the dual spinor [itex]\ \psi^{\dagger} \gamma_0 [itex], where [itex]\ \gamma_0 [itex] denotes the time-like Dirac matrix.

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

[itex] \rho = \bar\psi \psi[itex]

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