One-loop effective potential for scalar and vector fields on higher dimensional noncommutative flat manifolds

TL;DR

This paper calculates the one-loop effective potential for scalar and vector fields on higher-dimensional noncommutative manifolds, revealing unique regularization challenges due to noncommutativity.

Contribution

It introduces a zeta function approach to evaluate effective potentials on noncommutative manifolds, highlighting issues with regularity at the origin.

Findings

Zeta function may be irregular at the origin in this context

Heat-kernel trace exhibits a logarithmic term in short-time expansion

Implications for quantum field theories on noncommutative spaces

Abstract

The effective potentials for massless scalar and vector quantum field theories on D dimensional manifolds with p compact noncommutative extra dimensions are evaluated by means of dimensional regularization implemented by zeta function techniques. It is found that the zeta function associated with the one-loop operator may not be regular at the origin. Thus, the related heat-kernel trace has a logarithmic term in the short t asymptotics expansion. Consequences of this fact are briefly discussed.