Berezin quantization of the Schrodinger algebra

Details Berezin quantization of the Schrodinger algebra Berezin quantization of the Schrodinger algebra

2000-09-08

arxiv.org/abs/math-ph/0009010v1

Infinite Dimensional Analysis, Quantum Probability, and Related Topics, 6, No. 1 (2003) 57-71

Physics

Mathematical Physics

19 pages, LaTeX

Scientific paper

We examine the Schrodinger algebra in the framework of Berezin quantization. First, the Heisenberg-Weyl and sl(2) algebras are studied. Then the Berezin representation of the Schrodinger algebra is computed. In fact, the sl(2) piece of the Schrodinger algebra can be decoupled from the Heisenberg component. This is accomplished using a special realization of the sl(2) component that is built from the Heisenberg piece as the quadratic elements in the Heisenberg-Weyl enveloping algebra. The structure of the Schrodinger algebra is revealed in a lucid way by the form of the Berezin representation.

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