On phase-space representations of quantum mechanics

We discuss a class of representations of quantum mechanics which uses funct ions defined on a parameter space to represent observable quantities. We sh ow that infinitesimal canonical transformations could be used to introduce a phase-space-like structure consistent with the requirements of quantum me chanics. The resulting family of phase-space representations of quantum mec hanics contains many well-known representations as special cases, e.g., the Weyl-Wigner-Moyal, normal and antinormal one. It is also flexible enough t o represent, e.g., PT-symmetric theories, introduced recently within the co ntext of non-Hermitian quantum mechanics. (C) 2001 Elsevier Science B.V. Al l rights reserved.