Generalized Weyl-Wigner-Moyal Formalism and Topological Groups
Mathematical Physics
2013-02-05 v1 math.MP
Abstract
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"
Cite
@article{arxiv.1012.5768,
title = {Generalized Weyl-Wigner-Moyal Formalism and Topological Groups},
author = {J. J. Sławianowski and V. Kovalchuk and A. Martens and B. Gołubowska and E. E. Rożko},
journal= {arXiv preprint arXiv:1012.5768},
year = {2013}
}
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