83 research outputs found
Spectral triples and Toeplitz operators
We give examples of spectral triples, in the sense of A. Connes, constructed
using the algebra of Toeplitz operators on smoothly bounded strictly
pseudoconvex domains in , or the star product for the Berezin-Toeplitz
quantization. Our main tool is the theory of generalized Toeplitz operators on
the boundary of such domains, due to Boutet de Monvel and Guillemin.Comment: 31 page
-deformation, affine group and spectral triples
A regular spectral triple is proposed for a two-dimensional
-deformation. It is based on the naturally associated affine group ,
a smooth subalgebra of , and an operator \caD defined by two
derivations on this subalgebra. While \caD has metric dimension two, the
spectral dimension of the triple is one. This bypasses an obstruction described
in \cite{IochMassSchu11a} on existence of finitely-summable spectral triples
for a compactified -deformation.Comment: 29 page
Spectral action in noncommutative geometry: An example
International audienceThis is a report on a joint work [12] with D. Essouabri, C. Levy and A. Sitarz. The spectral action on noncommutative torus is obtained, using a Chamseddine–Connes formula via computations of zeta functions. The importance of a Diophantine condition is outlined as far as the difficulties to go beyond. Some results on holomorphic continuation of series of holomorphic functions are presented
Spectral action on noncommutative torus
The spectral action on noncommutative torus is obtained, using a
Chamseddine--Connes formula via computations of zeta functions. The importance
of a Diophantine condition is outlined. Several results on holomorphic
continuation of series of holomorphic functions are obtained in this context.Comment: 57 page
Moyal Planes are Spectral Triples
Axioms for nonunital spectral triples, extending those introduced in the
unital case by Connes, are proposed. As a guide, and for the sake of their
importance in noncommutative quantum field theory, the spaces endowed
with Moyal products are intensively investigated. Some physical applications,
such as the construction of noncommutative Wick monomials and the computation
of the Connes--Lott functional action, are given for these noncommutative
hyperplanes.Comment: Latex, 54 pages. Version 3 with Moyal-Wick section update
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