Quantum mechanics on Riemannian manifold in Schwinger's quantization approach IV - Quantum mechanics of superparticle

In this paper we extend Schwinger's quantization approach to the case of a supermanifold considered as a coset space of the Poincare group by the Lorentz group. In terms of coordinates parameterizing a supermanifold, quantum mechanics for a superparticle is constructed. As in models related to the usual Riemannian manifold, the key role in the analysis is played by Killing vectors. The main feature of quantum theory on the supermanifold consists of the fact that the spatial coordinates do not commute and therefore are represented on wave functions by integral operators.