135 citations · 321 across the 10 of their papers we have counts for
10 papers
Multipliers of Hilbert algebras and deformation quantization
Axel de Goursac
In this paper, we introduce the notion of multiplier of a Hilbert algebra. The space of bounded multipliers is a semifinite von Neumann algebra isomorphic to the left von Neumann a…
Non-formal deformation quantization and star-exponential of the Poincare Group
Pierre Bieliavsky, Axel de Goursac, Florian Spinnler
We recall the construction of non-formal deformation quantization of the Poincare Group ISO(1,1) on its coadjoint orbit and exhibit the associated non-formal star-exponentials.
Harmonic analysis on homogeneous complex bounded domains and noncommutative geometry
Pierre Bieliavsky, Victor Gayral, Axel de Goursac +1
We define and study a noncommutative Fourier transform on every homogeneous complex bounded domain. We then give an application in noncommutative differential geometry by defining…
Non-formal deformation quantization of abelian supergroups
Axel de Goursac
We review recent works concerning deformation quantization of abelian supergroups. Indeed, we expose the construction of an induced representation of the Heisenberg supergroup and…
Noncommutative field theories with harmonic term
Axel de Goursac
The UV-IR mixing of scalar field theory on the Moyal space is removed by the harmonic term, so that the theory is renormalizable. We will present different properties of this scala…
Noncommutative geometry, gauge theory and renormalization
Axel de Goursac
Nowadays, noncommutative geometry is a growing domain of mathematics, which can appear as a promising framework for modern physics. Quantum field theories on "noncommutative spaces…