Symplectic areas, quantization, and dynamics in electromagnetic fields

Details Symplectic areas, quantization, and dynamics in electromagnetic fields Symplectic areas, quantization, and dynamics in electromagnetic fields

2000-02-15

arxiv.org/abs/quant-ph/0002041v1

J. Math. Phys. 43:756-788, 2002

Physics

Quantum Physics

39 pages, 17 figures

Scientific paper

10.1063/1.1426688

A gauge invariant quantization in a closed integral form is developed over a linear phase space endowed with an inhomogeneous Faraday electromagnetic tensor. An analog of the Groenewold product formula (corresponding to Weyl ordering) is obtained via a membrane magnetic area, and extended to the product of N symbols. The problem of ordering in quantization is related to different configurations of membranes: a choice of configuration determines a phase factor that fixes the ordering and controls a symplectic groupoid structure on the secondary phase space. A gauge invariant solution of the quantum evolution problem for a charged particle in an electromagnetic field is represented in an exact continual form and in the semiclassical approximation via the area of dynamical membranes.

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