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arXiv · 1311.3115

Natural star-products on symplectic manifolds and related quantum mechanical operators

Maciej Blaszak·Ziemowit Domanski
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Abstract

In this paper is considered a problem of defining natural star-products on symplectic manifolds, admissible for quantization of classical Hamiltonian systems. First, a construction of a star-product on a cotangent bundle to an Euclidean configuration space is given with the use of a sequence of pair-wise commuting vector fields. The connection with a covariant representation of such a star-product is also presented. Then, an extension of the construction to symplectic manifolds over flat and non-flat pseudo-Riemannian configuration spaces is discussed. Finally, a coordinate free construction of related quantum mechanical operators from Hilbert space over respective configuration space is presented.

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Maciej Blaszak, Ziemowit Domanski. 2013-11-13. Natural star-products on symplectic manifolds and related quantum mechanical operators. https://doi.org/10.1016/j.aop.2014.02.013

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