A gauge quantization prescription using a nilpotent BRST charge on the gauge-fixed state space. Physical states are represented by its BRST cohomology, usually at ghost number zero. Exact states decouple under suitable invariant-measure, boundary and positivity assumptions. Nilpotence alone does not prove positivity of the quotient or select its physical ghost-number sector.
For a relativistic particle, the Hamiltonian gauge parameter changes the worldline einbein by its time derivative. Fixing the einbein to a constant therefore gives a Faddeev-Popov determinant of , represented by anticommuting FP ghosts. Gauge zero modes and the proper-time modulus are treated separately. The displayed phase convention gives the odd canonical bracket .
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BRST quantization is a formalism used in the field of quantum field theory to handle systems with gauge symmetries. It is named after the physicists Bonora, Reisz, Sirlin, and Tyutin, who contributed to its development. BRST stands for Becchi-Rouet-Stora-Tyutin, referring to the key researchers who formulated the method. The motivation for BRST quantization arises from the challenges associated with quantizing gauge theories.