Applications of the theory of the metaplectic representation to quadratic Hamiltonians on the two-dimensional Euclidean space
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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.
- Tokyo Sugaku Kaisya Zasshi
Tokyo Sugaku Kaisya Zasshi 52(2), 269-292, 2000-04
The Mathematical Society of Japan