Abstract
We discuss a class of representations of quantum mechanics which uses functions defined on a parameter space to represent observable quantities. We show that infinitesimal canonical transformations could be used to introduce a phase-space-like structure consistent with the requirements of quantum mechanics. The resulting family of phase-space representations of quantum mechanics contains many well-known representations as special cases, e.g., the Weyl–Wigner–Moyal, normal and antinormal one. It is also flexible enough to represent, e.g., PT -symmetric theories, introduced recently within the context of non-Hermitian quantum mechanics.
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