# What is the major difference between Dirac and BRST quantization of point particle?

I have derived the action for the bosonic point particle and now I want to quantize it but there are two formalism: one is Dirac and the other one is BRST. I want to know what is the major difference between these two mechanisms?

• What exactly do you mean by "major difference", given that both approaches must yield the same final theory, else one of them is not different, but simply wrong? – ACuriousMind Nov 30 '17 at 8:34

I) For a general Hamiltonian gauge theory,

1. the Dirac/Bergmann analysis with the Gupta-Bleuler condition ("old quantization method")

is generalized/refined by

1. the Hamiltonian BRST quantization ("new quantization method") with a nilpotent BRST charge $Q$. Physical states are described by the BRST-cohomology.

If the gauge algebra structure is complicated enough, the old method is insufficient.

II) For the BRST formulation of a point particle, see e.g. my Phys.SE answer here.

References:

1. M. Henneaux & C. Teitelboim, Quantization of Gauge Systems, 1994.