Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-01-11
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.
Chepilko N. M.
Romanenko A. V.
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