Heat Trace Asymptotics on Noncommutative Spaces

Abstract

This is a mini-review 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.

This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (20)

• Deformation quantization of Poisson manifolds, I
• The Spectral Action Principle
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations
• Induced Gauge Theory on a Noncommutative Space
• Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
• Gauge Invariance, Finite Temperature and Parity Anomaly in D=3
• The spectral action for Moyal planes
• Non-commutative heat kernel
• Quantum noncommutative gravity in two dimensions
• The $a_5$ heat kernel coefficient on a manifold with boundary
• Trouble with space-like noncommutative field theory
• Heat kernel and number theory on NC-torus
• Noncommutative QFT and Renormalization
• Position-dependent noncommutative products: classical construction and field theory
• The asymptotics of the Laplacian on a manifold with boundary II
• On space-time noncommutative theories at finite temperature
• Heat kernel coefficients for compact fuzzy spaces
• Effective local geometric quantities in fuzzy spaces from heat kernel expansions
• Heat kernel of non-minimal gauge field kinetic operators on Moyal plane

Cited by in corpus (8)

• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• Noncommutative Geometries and Gravity
• Quantum corrections to the noncommutative kink
• Asymptotic and exact expansions of heat traces
• Nilpotent noncommutativity and renormalization
• Quantum aspects of a noncommutative supersymmetric kink
• A noncommutative integral on spectrally truncated spectral triples, and a link with quantum ergodicity
• Perturbation Theory on the Non-Commutative Plane with a Singular Potential