Supertrace and superquadratic Lie structure on the Weyl algebra, with applications to formal inverse Weyl transform

Georges Pinczon (1) , Rosane Ushirobira (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

Using the Moyal *-product and orthosymplectic supersymmetry, we construct a natural non trivial supertrace and an associated non degenerate invariant supersymmetric bilinear form for the Lie superalgebra structure of the Weyl algebra. 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.

Mots clés: Deformation quantization, supersymmetry, Weyl algebra, supertrace, renormalization, formal inverse Weyl transform

Domaines: Théorie des représentations [math.RT]

Georges Pinczon, Rosane Ushirobira. Supertrace and superquadratic Lie structure on the Weyl algebra, with applications to formal inverse Weyl transform. Letters in Mathematical Physics, 2005, 74 (3), pp.263. ⟨10.1007/S11005-005-0029-3⟩. ⟨hal-00438993⟩