Quantization of a spinning particle in an arbitrary background

This paper is a natural continuation of the papers by Gavrilov and Gitman ( 2000 Class. Quantum Grav, 17 L133, 2000 Int. J. Mod. Phys. A 15 4499) devot ed to relativistic particle quantization. Here we generalize the problem, c onsidering the quantization of a spinning particle in an arbitrary gravitat ional background. The non-triviality of such a generalization is related to the necessity of solving complicated ordering problems. Similar to the fla t-spacetime case, we show in the course of the canonical quantization how a consistent relativistic quantum mechanics of a spinning particle in gravit ational and electromagnetic backgrounds can be constructed.