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?
I) For a general Hamiltonian gauge theory,
- the Dirac/Bergmann analysis with the Gupta-Bleuler condition ("old quantization method")
is generalized/refined by
- 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.
- M. Henneaux & C. Teitelboim, Quantization of Gauge Systems, 1994.