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

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.

9 pages, Latex AMS style, typos corrected, numerical coefficients corrected, references added

Cited by in corpus (4)

• Fluctuations of quantum fields via zeta function regularization
• Heat-kernel expansion on non compact domains and a generalised zeta-function regularisation procedure
• Effective action for scalar fields and generalised zeta-function regularisation
• When the Casimir energy is not a sum of zero-point energies