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

Details Quantum mechanics on Riemannian manifold in Schwinger's quantization approach IV Quantum mechanics on Riemannian manifold in Schwinger's quantization approach IV

2002-01-11

arxiv.org/abs/hep-th/0201074v1

Eur.Phys.J.C22:601-611,2001

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, Springer-Verlag Journal Style, no figures

Scientific paper

10.1007/s100520100807

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 parametrizing a supermanifold, quantum mechanics for a superparticle is constructed. As in models related to the usual Riemannian manifold, the key role in analyzes is played by Killing vectors. The main feature of quantum theory on the supermanifold consists of the fact that the spatial coordinates are not commute with each other and therefore are represented on wave functions by integral operators.

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