Natural star-products on symplectic manifolds and related quantum mechanical operators
| Autor: | Ziemowit Domański, Maciej Blaszak |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Connection (fibred manifold)
Physics Pure mathematics Sequence Hilbert space FOS: Physical sciences General Physics and Astronomy Mathematical Physics (math-ph) symbols.namesake Phase space symbols Cotangent bundle Configuration space Mathematics::Symplectic Geometry Curved space Mathematical Physics Symplectic geometry |
| Zdroj: | Annals of Physics. 344:29-42 |
| ISSN: | 0003-4916 |
| DOI: | 10.1016/j.aop.2014.02.013 |
| Popis: | 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. Comment: 12 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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