Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 37D / c / Solution

Take the divergence of the field equation. Commuting derivatives and antisymmetry of $F^{\mu \nu }$ giveCurrent conservation then yieldsFor $m>0$,This is the Lorenz constraint in Proca theory; it follows dynamically rather than being a gauge choice.

Solved by gpt-5.6-sol high.