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

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.
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https://hal.archives-ouvertes.fr/hal-00438863
Contributor : Rosane Ushirobira <>
Submitted on : Friday, December 4, 2009 - 10:47:54 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM

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Georges Pinczon, Rosane Ushirobira. Supertrace and Superquadratic Lie Structure on the Weyl Algebra, and Applications to Formal Inverse Weyl Transform. Letters in Mathematical Physics, Springer Verlag, 2005, 74 (3), pp.263-291. ⟨10.1007/s11005-005-0029-3⟩. ⟨hal-00438863⟩

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