Resummed heat kernel and effective action for Yukawa and QED

Abstract

In this letter, we prove the existence of resummed expressions for the diagonal of the heat kernel and theeffective action of a quantum field which interacts with a scalar or an electromagnetic background. Working inan arbitrary number of spacetime dimensions, we propose an Ansatz beyond the Schwinger–DeWitt proposal,effectively resumming an infinite number of invariants which can be constructed from powers of the background,as well as its first and second derivatives in the Yukawa case. This provides a proof of the recent conjecture that𝜇𝜈 ̃𝜇𝜈all terms containing the invariants 𝐹𝜇𝜈 𝐹 and 𝐹𝜇𝜈 𝐹 in the proper-time series expansion of the SQED effectiveaction can be resummed. Possible generalizations and several applications are also discussed—in particular, the existence of an analogue of the Schwinger effect for Yukawa couplings.