Robert Mann - An Introduction to Particle Physics and the Standard Model · Problem 6

Testing QED — Robert Mann

Physics — Particle Physics · gauge-invariance-field-strength

Problem

(a) For a wavefunction

\Psi

with charge

e

show that

[D_\mu, D_\nu]\Psi = ieF_{\mu\nu}\Psi

(b) Use the preceding relation to show that

F_{\mu\nu}

is gauge-invariant. This provides another way to obtain the field strength of the electromagnetic potential.