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Complex Weyl symbols of metaplectic operators: An elementary approach

Cahen, Benjamin
2023
  • Controlled Vocabulary...

Abstract
We give explicit formulas for the Berezin symbols and the complex Weyl symbols of the metaplectic representation operators by using the holomorphic representations of the Jacobi group. Then we recover some known formulas for the symbols of the metaplectic operators in the classical Weyl calculus, in particular for the classical Weyl symbol of the exponential of an operator whose Weyl symbol is a quadratic form.
DOI
10.13137/2464-8728/35486
Soggetti
  • Complex Weyl calculus...

  • Weyl correspondence

  • Fock space

  • Bargmann- Fock repres...

  • Berezin quantization

  • Heisenberg group

  • metaplectic represent...

  • symplectic group

  • Jacobi group

  • reproducing kernel Hi...

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