Advanced Quantum Mechanics Schwabl · Problem 10.1

Symmetries and Further Properties of the Dirac Equation

Physics — Quantum Mechanics · gordon-identity-dirac-equation

Problem

Prove the Gordon identity (10.1.5), which states that, for two positive energy solutions of the free Dirac equation,

u_r(p)

and

u_{r'}(p)

\bar{u}_r(p)\gamma^\mu u_{r'}(q) = \frac{1}{2m}\bar{u}_r(p)[(p+q)^\mu + \mathrm{i}\sigma^{\mu\nu}(p-q)_\nu]u_{r'}(q)\,.