Letters in Mathematical Physics

, Volume 74, Issue 3, pp 263–291 | Cite as

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

  • G. PinczonEmail author
  • R Ushirobira


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


Deformation quantization supersymmetry Weyl algebra supertrace renormalization formal inverse Weyl transform 


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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Institut de Mathématiques de BourgogneUniversité de BourgogneDijon CedexFrance

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