Non-commutative heat kernel

Abstract

We consider a natural generalisation of the Laplace type operators for the case of non-commutative (Moyal star) product. We demonstrate existence of a power law asymptotic expansion for the heat kernel of such operators on T^n. First four coefficients of this expansion are calculated explicitly. We also find an analog of the UV/IR mixing phenomenon when analysing the localised heat kernel.

10 pp; v2: math improved, references added, to be published in LMP

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Cited by in corpus (34)

• Induced Gauge Theory on a Noncommutative Space
• The spectral action for Moyal planes
• Quantum noncommutative gravity in two dimensions
• Heat kernel and number theory on NC-torus
• Heat kernel, effective action and anomalies in noncommutative theories
• Noncommutative QFT and Renormalization
• Noncommutative Induced Gauge Theories on Moyal Spaces
• Space-time non-commutativity tends to create bound states
• Covariant derivative expansion of the heat kernel
• Worldline approach to noncommutative field theory
• Quantum corrections to the noncommutative kink
• Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
• Derivative expansion of the heat kernel in curved space
• Heat Trace Asymptotics on Noncommutative Spaces
• Construction of the effective action in nonanticommutative supersymmetric field theories
• On space-time noncommutative theories at finite temperature
• Asymptotic and exact expansions of heat traces
• Heat kernel coefficients for compact fuzzy spaces
• Effective local geometric quantities in fuzzy spaces from heat kernel expansions
• From homotopy to Ito calculus and Hodge theory
• Renormalization on noncommutative torus
• Nilpotent noncommutativity and renormalization
• Heat kernel of non-minimal gauge field kinetic operators on Moyal plane
• Quantum group symmetry and discrete scale invariance: Spectral aspects
• Induced Chern-Simons action on noncommutative torus
• The invariant factor of the chiral determinant
• One-loop effective potential in $\mathcal{N}=1/2$ generic chiral superfield model
• Constraints, gauge symmetries, and noncommutative gravity in two dimensions
• Worldline approach to the Grosse-Wulkenhaar model
• Induced Gauge Theory on a Noncommutative Space
• On space-time noncommutative U(1) model at high temperature
• Zeta-regularization and the heat-trace on some compact quantum semigroups
• Fractality in Cosmic Topology Models with Spectral Action Gravity
• Spectral action in noncommutative geometry: An example