Gaussian transform of the Weil representation

Details Gaussian transform of the Weil representation Gaussian transform of the Weil representation

2006-01-12

arxiv.org/abs/math-ph/0601029v1

Short version: Funct. Anal. Appl. 40(2006), No. 3, 90--93.

Physics

Mathematical Physics

21 pages

Scientific paper

A description is given of the image of the Weil representation of the symplectic group in the Schwartz space and in the space of tempered distributions under the Gaussian integral transform. We also discuss the problem of infinite dimensional generalization of the Weil representation in the Schwartz space, in order to construct appropriate quantization of free scalar field.

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