Derivative expansion of the heat kernel in curved space

Abstract

The heat kernel in curved space-time is computed to fourth order in a strict expansion in the number of covariant derivatives. The computation is made for arbitrary non abelian gauge and scalar fields and for the Riemann connection in the coordinate sector. The expressions obtained hold for arbitrary tensor representations of the matter field. Complete results are presented for the diagonal matrix elements and for the trace of the heat kernel operator. In addition, Chan's formula is extended to curved space-time. As a byproduct, the bosonic effective action is also obtained to fourth order.

11 pages, no figures. Discussion added at the end of section II about the nature of the derivative expansion. To appear in Phys.Rev.D

References in corpus (2)

• The method of covariant symbols in curved space-time
• Supersymmetry of Noncompact MQCD-like Membrane Instantons and Heat Kernel Asymptotics

Cited by in corpus (5)

• The number of eigenstates: counting function and heat kernel
• Direct construction of the effective action of chiral gauge fermions in the anomalous sector
• Renormalization of vector fields with mass-like coupling in curved spacetime
• Quantum Corrections in Classicalon Theories
• Non-minimal non-Abelian quantum vector fields in curved spacetime