Deformation Quantization for Heisenberg Supergroup

Bieliavsky, Pierre;Marcillaud de Goursac, Axel;Tuynman, Gijs
(2012) Journal of Functional Analysis — Vol. 263, n° 3, p. 549-603 (2012)

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Authors
  • Bieliavsky, PierreUCLouvain
    Author
  • Marcillaud de Goursac, AxelUCLouvain
    Author
  • Tuynman, GijsUniversité de Lille I
    Author
Abstract
We construct a non-formal deformation machinery for the actions of the Heisenberg supergroup analogue to the one developed by M. Rieffel for the actions of R^d. However, the method used here differs from Rieffel’s one: we obtain a Universal Deformation Formula for the actions of R^{m|n} as a byproduct of Weyl ordered Kirillov’s orbit method adapted to the graded setting. To do so, we have to introduce the notion of C∗-superalgebra, which is compatible with the deformation, and which can be seen as corresponding to noncommutative superspaces. We also use this construction to interpret the renormalizability of a noncom- mutative quantum field theory.
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Bieliavsky, P., Marcillaud de Goursac, A., & Tuynman, G. (2012). Deformation Quantization for Heisenberg Supergroup. Journal of Functional Analysis, 263(3), 549-603. https://doi.org/10.1016/j.jfa.2012.05.002 (Original work published 2012)