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Particles and Fields

Eur. Phys. J. C 22, 601-611 (2001)
DOI: 10.1007/s100520100807

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

Quantum mechanics of superparticle
N.M. Chepilko1 and A.V. Romanenko2

1  Physics Institute of the Ukrainian Academy of Sciences, Kyiv-03 028, Ukraine
2  Kyiv Taras Shevchenko University, Department of Physics, Kyiv-03 022, Ukraine

(Received: 22 June 2001 / Revised version: 4 October 2001 / Published online: 23 November 2001 - © Springer-Verlag / Società Italiana di Fisica 2001 )

In this paper we extend Schwinger's quantization approach to the case of a supermanifold considered as a coset space of the Poincaré 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.

© Società Italiana di Fisica, Springer-Verlag 2001