1996/08/28 by Frank Antonsen
Physics and Astronomy · #quant-ph
published as Int.J.Theor.Phys. 37 (1998) 697-758 · pure LaTeX
arxiv created 1996/08/28 · arxiv updated 2009/12/01
We first introduce the Wigner-Weyl-Moyal formalism for a theory whose phase-space is an arbitrary Lie algebra. We also generalize to quantum Lie algebras and to supersymmetric theories. It turns out that the non-commutativity leads to a deformation of the classical phase-space: instead of being a vector space it becomes a manifold, the topology of which is given by the commutator relations. It is shown in fact that the classical phase-space, for a semi-simple Lie algebra, becomes a homogenous symplectic manifold. The symplectic product is also deformed. We finally make some comments on how to generalize to C^*-algebras and other operator algebras too.