Resummed effective actions and heat kernels: the Worldline approach and Yukawa assisted pair creation

TL;DR

This paper develops a Worldline Formalism-based method to compute resummed effective actions and heat kernels for scalar fields with Yukawa interactions, revealing how complex backgrounds influence vacuum instability and pair production.

Contribution

It introduces a resummation technique within the Worldline Formalism for scalar fields coupled to Yukawa backgrounds, enabling detailed analysis of vacuum instability and pair creation.

Findings

Resummed expressions for effective action and heat kernel derived.

Vacuum instability and pair production probabilities computed.

Rapidly varying backgrounds significantly enhance pair creation.

Abstract

We adapt the Worldline Formalism to obtain resummed expressions for the effective action and the heat kernel of a quantum scalar field coupled to a Yukawa background. The resummation includes all the invariants built from powers, first derivatives and second derivatives of the latter. Using such results, we compute the instability of the vacuum computing the vacuum persistence amplitude and the corresponding Schwinger pair production probability. We show that the inclusion of an additional, rapidly varying background can greatly enhance the production of pairs.