Supertrace and Superquadratic Lie Structure on the Weyl Algebra,and Applications to Formal Inverse Weyl Transform |
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Authors: | Email author" target="_blank">G?PinczonEmail author R?Ushirobira |
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Institution: | (1) Institut de Mathématiques de Bourgogne, Université de Bourgogne, B.P. 47870, F-21078 Dijon Cedex, France |
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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
Mathematics Subject Classification: 53D55, 17B05, 17B10, 17B20, 17B60, 17B65 |
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Keywords: | Deformation quantization supersymmetry Weyl algebra supertrace renormalization formal inverse Weyl transform |
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