30 citations · 85 across the 9 of their papers we have counts for
11 papers
Traces of holomorphic families of operators on the noncommutative torus and on Hilbert modules
Sara Azzali, Cyril Lévy, Carolina Neira Jiménez +1
We revisit traces of holomorphic families of pseudodifferential operators on a closed manifold in view of geometric applications. We then transpose the corresponding analytic const…
The canonical trace and the noncommutative residue on the noncommutative torus
Cyril Levy, Carolina Neira Jiménez, Sylvie Paycha
Using a global symbol calculus for pseudodifferential operators on tori, we build a canonical trace on classical pseudodifferential operators on noncommutative tori in terms of a c…
Global and local aspects of spectral actions
Bruno Iochum, Cyril Levy, Dmitri Vassilevich
The principal object in noncommutatve geometry is the spectral triple consisting of an algebra A, a Hilbert space H, and a Dirac operator D. Field theories are incorporated in this…
Spectral action beyond the weak-field approximation
B. Iochum, C. Levy, D. Vassilevich
The spectral action for a non-compact commutative spectral triple is computed covariantly in a gauge perturbation up to order 2 in full generality. In the ultraviolet regime, $p\to…
Spectral action for torsion with and without boundaries
Bruno Iochum, Cyril Levy, Dmitri Vassilevich
We derive a commutative spectral triple and study the spectral action for a rather general geometric setting which includes the (skew-symmetric) torsion and the chiral bag conditio…
Spectral triples and manifolds with boundary
Bruno Iochum, Cyril Levy
We investigate manifolds with boundary in noncommutative geometry. Spectral triples associated to a symmetric differential operator and a local boundary condition are constructed.…