Weinberg propagator of free massive arbitrary spin particle from BFV – BRST path integral

The transition amplitude is obtained for free massive particle of arbitrary spin by calculating the path integral in the index–spinor formulation within BFV–BRST approach. None renormalizations of the path integral measure were applied. The calculation has given the Weinberg propagator written in index–free form with the use of index spinor. The choice of boundary conditions on the index spinor defines holomorphic or antiholo-morphic representation for canonical description of particle/antiparticle spin. In the development of extended object theories, the problem of covariant description of spinning particles, in particular the problem of covariant quantization of these particles, plays a double role. On the one hand, it is an educational model which allows one to illustrate the achieved progress and to train oneself in application of developing methods. On the other hand, it is a starting point and, in a certain sence, the wanted result of these theories intended to consistently realize the fundamental quantum and relativistic principles, so that one could speak about construction of the interaction theory for particles remaining the only actually observable manifestation of the fundamental structure of matter. It is well known that the spin can be described by commuting or anticommuting coordinates which can be applied both independently and as partners having the same rights in the content of supersymmetric theories. In the spin theory the bosonic and fermionic coordinates are most adequately used as spinors. It is not in contradiction with the existence of pseudoclassical 1