Applications of the theory of the metaplectic representation to quadratic Hamiltonians on the two-dimensional Euclidean space Dedicated to Professor Nobuyuki Ikeda on his seventieth birthday

Hiroyuki MATSUMOTO; Naomasa UEKI

doi:10.2969/jmsj/05220269

Applications of the theory of the metaplectic representation to quadratic Hamiltonians on the two-dimensional Euclidean space

Dedicated to Professor Nobuyuki Ikeda on his seventieth birthday

Hiroyuki MATSUMOTO, Naomasa UEKI

著者情報

キーワード: Spectrum, quadratic Hamiltonians, metaplectic representation, heat kernels, Wiener integrations, Lévy formula, Hermite polynomials

ジャーナルフリー

2000 年 52 巻 2 号 p. 269-292

DOI https://doi.org/10.2969/jmsj/05220269

詳細

抄録

The spectra of the quadratic Hamiltonians on the two-dimensional Euclidean space are determined completely by using the theory of the metaplectic representation. In some cases, the corresponding heat kernels are studied in connection with the well-definedness of the Wiener integrations. A proof of the Lévy formula for the stochastic area and a relation between the real and complex Hermite polynomials are given in our framework.

責任著者(Corresponding author)

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