T. A. Osborn Digital Library

The Wigner-Weyl Transform on Tori and Connected Graph Propagator Representations

T. A. Osborn1, F. H. Molzahn2
1Department of Physics, University of Manitoba, Winnipeg, MB, Canada
2Department of Applied Mathematics, University of Manitoba, Winnipeg, MB, Canada
Report: IMA Preprint #758 | Journal: IMA Preprint Series | Year: 1990 | Pages: 36

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Abstract

For a quantum system set on the manifold T^e × R^d, a connected graph expansion is obtained for the Schrödinger propagator with scalar interactions. A definition of the Wigner transform suitable for the torus is proposed. The graphical propagator expansion is extended to the Wigner representation. An explicit tree graph formula for the 'phase action' in R^d is extracted as one particular application.

Keywords

Wigner Transform Weyl Transform Tori Connected Graphs Propagators Phase Space Schrödinger Equation Semiclassical

Metadata

Report NumberIMA Preprint #758
Date1990
PublisherInstitute for Mathematics and its Applications, University of Minnesota
LanguageEnglish
Pages36

Citation

T. A. Osborn, F. H. Molzahn, "The Wigner-Weyl Transform on Tori and Connected Graph Propagator Representations," IMA Preprint Series #758 (1990).

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