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 twister-like approach by the use of the BRST-BFV-quantization prescription. In the course of the Hamiltonian analysis we observe links between various formulations of the twister-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 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 twister-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 twister-like particle propagator in D = 3, 4, 6 space-time dimensions and show that it coincides with that of a conventional massless bosonic particle.