Talk:Dirac adjoint

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Unless there are objections, I shall replace the Usage section with the below. The probability density is incorrect in the current version. Some formatting may need to be improved. Xxanthippe 05:56, 25 February 2007 (UTC)

[edit] Usage

Using the Dirac adjoint, the conserved probability four-current density for a spin-1/2 particle field

j^\mu = (c\rho, j)\,

where \rho\, is the probability density and j the probability current 3-density can be written as

j^\mu = c\bar\psi\gamma^\mu\psi

where c is the speed of light. Taking μ = 0 and using the relation for Gamma matrices

\left( \gamma^0 \right)^2 = I \,

the probability density becomes

\rho = \psi^\dagger\psi\, .