A Weyl Calculus on Symplectic Phase Space
Maurice De Gosson
TL;DR
This paper develops a Weyl calculus on symplectic phase space by defining a twisted Weyl symbol for metaplectic operators and establishing a covariant algebra of pseudo-differential operators.
Contribution
It introduces a new index for symplectic paths and constructs a covariant algebra of pseudo-differential operators on symplectic space.
Findings
Defined an index for symplectic paths related to Conley-Zehnder index
Established a covariant algebra of pseudo-differential operators
Analyzed the twisted Weyl symbol of metaplectic operators
Abstract
We study the twisted Weyl symbol of metaplectic operators; this requires the definition of an index for symplectic paths related to the Conley-Zehnder index. We thereafter define a metaplectically covariant algebra of pseudo-differential operators acting on functions on symplectic space.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Advanced Topics in Algebra