Deformation Quantization for Heisenberg Supergroup

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 noncommutative Quantum Field Theory.

49 pages

References in corpus (6)

• Noncommutative Induced Gauge Theory
• Induced Gauge Theory on a Noncommutative Space
• Noncommutative geometry, gauge theory and renormalization
• Deformation Quantization for Actions of Kählerian Lie Groups
• On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
• Hochschild Cohomology and Deformations of Clifford-Weyl Algebras

Cited by in corpus (11)

• Harmonic analysis on homogeneous complex bounded domains and noncommutative geometry
• Cohomology of Heisenberg Lie Superalgebras
• Fréchet Quantum Supergroups
• Renormalization of the commutative scalar theory with harmonic term to all orders
• Deformation Quantization for actions of ${\mathbb{Q}}_p^d$
• Noncommutative Supergeometry and Quantum Supergroups
• Multipliers of Hilbert algebras and deformation quantization
• Super unitary representations revisited
• Non-formal deformation quantization and star-exponential of the Poincare Group
• Quantum Kählerian Lie groups from multiplicative unitaries
• Star Products that can not be induced by Drinfel'd Twists