Results 1  10
of
18
Spectral action on SUq(2)
, 803
"... The spectral action on the equivariant real spectral triple over A ( SUq(2) ) is computed explicitly. Properties of the differential calculus arising from the Dirac operator are studied and the results are compared to the commutative case of the sphere S 3. ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
(Show Context)
The spectral action on the equivariant real spectral triple over A ( SUq(2) ) is computed explicitly. Properties of the differential calculus arising from the Dirac operator are studied and the results are compared to the commutative case of the sphere S 3.
Heat Trace Asymptotics on Noncommutative Spaces
, 2007
"... This is a minireview of the heat kernel expansion for generalized Laplacians on various noncommutative spaces. Applications to the spectral action principle, renormalization of noncommutative theories and anomalies are also considered. ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
(Show Context)
This is a minireview of the heat kernel expansion for generalized Laplacians on various noncommutative spaces. Applications to the spectral action principle, renormalization of noncommutative theories and anomalies are also considered.
NONCOMMUTATIVE MIXMASTER COSMOLOGIES
, 1203
"... Abstract. In this paper we investigate a variant of the classical mixmaster universe model of anisotropic cosmology, where the spatial sections are noncommutative 3tori. We consider ways in which the discrete dynamical system describing the mixmaster dynamics can be extended to act on the noncommut ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper we investigate a variant of the classical mixmaster universe model of anisotropic cosmology, where the spatial sections are noncommutative 3tori. We consider ways in which the discrete dynamical system describing the mixmaster dynamics can be extended to act on the noncommutative torus moduli, and how the resulting dynamics differs from the classical one, for example, in the appearance of exotic smooth structures. We discuss properties of the spectral action, focussing on how the slowroll inflation potential determined by the spectral action affects the mixmaster dynamics. We relate the model to other recent results on spectral action computation and we identify other physical contexts in which this model may be relevant.
A ChernSimons action for noncommutative spaces in general with the example SU q(2). 2012. arXiv
"... ar ..."
(Show Context)
Spectral Geometry
, 2011
"... The goal of these lectures is to present some fundamentals of noncommutative geometry looking around its spectral approach. Strongly motivated by physics, in particular by relativity and quantum mechanics, Chamseddine and Connes have defined an action based on spectral considerations, the socalled ..."
Abstract
 Add to MetaCart
(Show Context)
The goal of these lectures is to present some fundamentals of noncommutative geometry looking around its spectral approach. Strongly motivated by physics, in particular by relativity and quantum mechanics, Chamseddine and Connes have defined an action based on spectral considerations, the socalled spectral action. The idea here is to review the necessary tools which are behind this spectral action to be able to compute it first in the case of Riemannian manifolds (Einstein–Hilbert action). Then, all primary objects defined for manifolds will be generalized to reach the level of noncommutative geometry via spectral triples, with the concrete analysis of the noncommutative torus which is a deformation of the ordinary one. The basics ingredients such as Dirac operators, heat equation asymptotics, zeta functions, noncommutative residues, pseudodifferential operators, or Dixmier traces will be presented and studied within the framework of operators on Hilbert spaces. These notions are appropriate in noncommutative geometry to tackle the case where the space is swapped with an algebra like for instance the noncommutative torus.