Covariant geometric quantization of non-relativistic Hamiltonian mechanics

Details Covariant geometric quantization of non-relativistic Hamiltonian mechanics Covariant geometric quantization of non-relativistic Hamiltonian mechanics

2000-12-07

arxiv.org/abs/quant-ph/0012036v2

Physics

Quantum Physics

17 pages

Scientific paper

We provide geometric quantization of the vertical cotangent bundle V^*Q equipped with the canonical Poisson structure. This is a momentum phase space of non-relativistic mechanics with the configuration bundle Q -> R. The goal is the Schrodinger representation of V^*Q. We show that this quantization is equivalent to the fibrewise quantization of symplectic fibres of V^*Q -> R, that makes the quantum algebra of non-relativistic mechanics an instantwise algebra. Quantization of the classical evolution equation defines a connection on this instantwise algebra, which provides quantum evolution in non-relativistic mechanics as a parallel transport along time.

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