Path integrals and pseudoclassical description for spinning particles in arbitrary dimensions

The propagator of a spinning particle in an external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has distinct solutions in even and odd dimensions. In even dimensions the representation is just a generalization of the one in four dimensions (which is already known). In this case the gauge invariant part of the effective action in the path integral has the form of the standard (Berezin-Marinov) pseudoclassical action. In odd dimensions the solution is presented for the first time and, in particular, it turns out that the gauge invariant part of the effective action differs from the standard one. We propose this new action as a candidate to describe spinning particles in odd dimensions. Studying the Hamiltonization of the pseudoclassical theory with the new action we show that the operator quantization leads to an adequate minimal quantum theory of spinning particles in odd dimensions. Finally the consideration is generalized for the case of a particle with an anomalous magnetic moment.