Generalized Weyl-Wigner-Moyal Formalism and Topological Groups

Details Generalized Weyl-Wigner-Moyal Formalism and Topological Groups Generalized Weyl-Wigner-Moyal Formalism and Topological Groups

2010-12-28

arxiv.org/abs/1012.5768v1

Physics

Mathematical Physics

39

Scientific paper

10.1002/mma.1531

Discussed are some geometric aspects of the phase space formalism in quantum mechanics in the sense of Weyl, Wigner, Moyal and Ville. We analyze the relationship between this formalism and geometry of the Galilei group, classical momentum mapping, theory of unitary projective representations of groups, and theory of groups algebras. Later on we present some generalization to quantum mechanics on locally compact Abelian groups. It is based on Pontryagin duality. Indicated are certain physical aspects in quantum dynamics of crystal lattices, including the phenomenon of "Umklapp-Prozessen"

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