BRST symmetry

BRST symmetry is a nilpotent fermionic symmetry of a gauge-fixed action. Its differential $s$ replaces an infinitesimal gauge parameter by the ghost field and satisfies $s^2=0$.

A gauge-fixing fermion is a Grassmann-odd functional whose BRST transformation $s\Psi$ supplies the gauge-fixing and ghost terms. Nilpotence gives $s(s\Psi )=0$ immediately.

BRST cohomology identifies physical states and observables with BRST-closed objects modulo BRST-exact ones. A change of gauge-fixing fermion changes the action by a BRST-exact term and therefore leaves BRST-cohomology classes unchanged when the measure has no BRST anomaly.