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- Title
METAPLECTIC REPRESENTATION, CONLEY–ZEHNDER INDEX, AND WEYL CALCULUS ON PHASE SPACE.
- Authors
DE GOSSON, MAURICE
- Abstract
We define and study a metaplectically covariant class of pseudo-differential operators acting on functions on symplectic space and generalizing a modified form of the usual Weyl calculus. This construction requires a precise calculation of the twisted Weyl symbol of a class of generators of the metaplectic group and the use of a Conley–Zehnder type index for symplectic paths, defined without restrictions on the endpoint. Our calculus is related to the usual Weyl calculus using a family of isometries of L2(ℝn) on closed subspaces of L2(ℝ2n) and to an irreducible representation of the Heisenberg algebra distinct from the usual Schrödinger representation.
- Subjects
MATHEMATICAL analysis; WEYL theory of boundary value problems; INFINITESIMAL geometry; DIFFERENTIAL equations; ENGINEERING
- Publication
Reviews in Mathematical Physics, 2007, Vol 19, Issue 10, p1149
- ISSN
0129-055X
- Publication type
Article
- DOI
10.1142/S0129055X07003152