71 citations · 296 across the 20 of their papers we have counts for
9 papers · 1 filter
Fourier analysis on the affine group, quantization and noncompact Connes geometries
Victor Gayral, Jose M. Gracia-Bondia, Joseph C. Varilly
We find the Stratonovich-Weyl quantizer for the nonunimodular affine group of the line. A noncommutative product of functions on the half-plane, underlying a noncompact spectral tr…
Quantum field theory on projective modules
V. Gayral, J. -H. Jureit, T. Krajewski +1
We propose a general formulation of perturbative quantum field theory on (finitely generated) projective modules over noncommutative algebras. This is the analogue of scalar field…
Heat kernel and number theory on NC-torus
V. Gayral, B. Iochum, D. V. Vassilevich
The heat trace asymptotics on the noncommutative torus, where generalized Laplacians are made out of left and right regular representations, is fully determined. It turns out that…
Dixmier traces on noncompact isospectral deformations
Victor Gayral, Bruno Iochum, Joseph C. Varilly
We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group .…
Position-dependent noncommutative products: classical construction and field theory
V. Gayral, J. M. Gracia-Bondia, F. Ruiz Ruiz
We look in Euclidean for associative star products realizing the commutation relation , where the noncommutativity parameters depend on the pos…
Trouble with space-like noncommutative field theory
V. Gayral, J. M. Gracia-Bondia, F. Ruiz Ruiz
It is argued that the one-loop effective action for a space-like noncommutative scalar field theory does not exist. This indicates that such theories are not renormalizable already…