Worldline approach to noncommutative field theory

Abstract

The study of the heat-trace expansion in noncommutative field theory has shown the existence of Moyal nonlocal Seeley-DeWitt coefficients which are related to the UV/IR mixing and manifest, in some cases, the non-renormalizability of the theory. We show that these models can be studied in a worldline approach implemented in phase space and arrive to a master formula for the $n$-point contribution to the heat-trace expansion. This formulation could be useful in understanding some open problems in this area, as the heat-trace expansion for the noncommutative torus or the introduction of renormalizing terms in the action, as well as for generalizations to other nonlocal operators.

19 pages, version 2

References in corpus (1)

• Heat kernel and number theory on NC-torus

Cited by in corpus (12)

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• Berry phase in the phase space worldline representation: the axial anomaly and classical kinetic theory
• Local Neumann semitransparent layers: resummation, pair production and duality
• Renormalization on noncommutative torus
• Snyder-de Sitter meets the Grosse-Wulkenhaar model
• $U(N)$ Yang-Mills in non-commutative space time
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism