کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1856133 | 1529867 | 2014 | 14 صفحه PDF | دانلود رایگان |
• Invariant representations of natural star-products on symplectic manifolds are considered.
• Star-products induced by flat and non-flat connections are investigated.
• Operator representations in Hilbert space of considered star-algebras are constructed.
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.
Journal: Annals of Physics - Volume 344, May 2014, Pages 29–42