Advanced Quantum Mechanics Schwabl · Problem 11.3

Quantization of Relativistic Fields

Physics — Quantum Mechanics · time-reversal-dirac-theory

Problem

Show that, under a time-reversal operation

\mathcal{T}

, the four-current-density

j^\mu

in the Dirac theory satisfies

j^{\prime\,\mu}(\mathbf{x}, t) = j_\mu(\mathbf{x}, -t)\,.