2
$\begingroup$

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?

$\endgroup$
  • $\begingroup$ 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? $\endgroup$ – ACuriousMind Nov 30 '17 at 8:34
1
$\begingroup$

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.
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.