Volume 74, Number 3, 263-291, DOI: 10.1007/s11005-005-0029-3

Supertrace and Superquadratic Lie Structure on the Weyl Algebra, and Applications to Formal Inverse Weyl Transform

G. Pinczon and R Ushirobira

From the issue entitled "A Special Volume Dedicated to the Memory of F.A. Berezin"

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Abstract

Using the Moyal *-product and orthosymplectic supersymmetry, we construct a natural nontrivial supertrace and an associated nondegenerate invariant supersymmetric bilinear form for the Lie superalgebra structure of the Weyl algebra W. We decompose adjoint and twisted adjoint actions. We define a renormalized supertrace and a formal inverse Weyl transform in a deformation quantization framework and develop some examples

Keywords  Deformation quantization - supersymmetry - Weyl algebra - supertrace - renormalization - formal inverse Weyl transform

Mathematics Subject Classification: 53D55, 17B05, 17B10, 17B20, 17B60, 17B65

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