BRST quantization

Summary

BRST quantization handles gauge symmetry by enlarging the space of fields with ghosts and introducing an odd operator $Q$, the BRST operator, with $Q^2 = 0$. Physical states and physical observables are then the cohomology of $Q$: elements killed by $Q$, modulo elements of the form $Q(\cdot)$. In its simplest form the BRST complex is the Chevalley–Eilenberg complex that computes Lie algebra cohomology. Its degree-zero cohomology is the space of gauge-invariant states. The method makes the gauge-fixed theory consistent and is used to prove renormalizability and unitarity of non-abelian gauge theories.