On the BRST Quantization of the Massless Bosonic Particle in Twistor-Like Formulation

We study some features of bosonic particle path-integral quantization in a twistor-like approach by use of the BRST-BFV quantization prescription. In the course of the Hamiltonian analysis we observe links between various formulations of the twistor-like particle by performing a conversion of the Hamiltonian constraints of one formulation to another. A particular feature of the conversion procedure applied to turn the second-class constraints into the first-class constraints is that the simplest Lorentz-covariant way to do this is to convert a full mixed set of the initial first- and second-class constraints rather than explicitly extracting and converting only the second-class constraints. Another novel feature of the conversion procedure applied below is that in the case of the D=4 and D=6 twistor-like particle the number of new auxiliary Lorentz-covariant coordinates, which one introduces to get a system of first-class constraints in an extended phase space, exceeds the number of independent second-class constraints of the original dynamical system. We calculate the twistor-like particle propagator in D=3, 4 and 6 space-time dimensions and show, that it coincides with that of a conventional massless bosonic particle.