Principles of Quantum Mechanics · Problem 20.15

The Dirac Equation — R. Shankar

Physics — Quantum Mechanics · dirac-equation-charge-conjugation

Problem

The charge conjugate of a Dirac spinor ψ\psi is defined as ψc=CψˉT\psi^c = C\bar{\psi}^T where CC is the charge conjugation matrix satisfying CγμC−1=−(γμ)TC\gamma^\mu C^{-1} = -(\gamma^\mu)^T, and ψˉ=ψ†γ0\bar{\psi} = \psi^\dagger \gamma^0. Show that if ψ\psi satisfies the Dirac equation for a particle of charge ee in an electromagnetic field, then ψc\psi^c satisfies the Dirac equation for a particle of charge −e-e.

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