%0 Journal Article
%T Symplectic areas, quantization, and dynamics in electromagnetic fields
%A M. V. Karasev
%A T. A. Osborn
%J Mathematics
%D 2000
%I arXiv
%R 10.1063/1.1426688
%X 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.
%U http://arxiv.org/abs/quant-ph/0002041v1