Applications of the theory of the metaplectic representation to quadratic Hamiltonians on the two-dimensional Euclidean space (Q1574800)
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scientific article; zbMATH DE number 1490085
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Applications of the theory of the metaplectic representation to quadratic Hamiltonians on the two-dimensional Euclidean space |
scientific article; zbMATH DE number 1490085 |
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Applications of the theory of the metaplectic representation to quadratic Hamiltonians on the two-dimensional Euclidean space (English)
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12 March 2001
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The spectra of the quadratic Hamiltonians on the two-dimensional Euclidean space are completely determined 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 the framework of this paper.
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spectrum
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heat kernels
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Wiener integrations
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Lévy formula
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Hermite polynomials
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