Principles of Quantum Mechanics · Problem 20.3

The Dirac Equation — R. Shankar

Physics — Quantum Mechanics · dirac-equation-covariant-form

Problem

Show that the Dirac equation can be written in the covariant form

(i\gamma^\mu \partial_\mu - \kappa)\psi = 0

where

\kappa = mc/\hbar

and the gamma matrices

\gamma^\mu

satisfy the anticommutation relations

\{\gamma^\mu, \gamma^\nu\} = 2g^{\mu\nu}.