Pair Production in Real Proper Time and Unitarity Without Borel Ambiguity

TL;DR

This paper develops a real proper time approach to analyze scalar pair production in electromagnetic fields, ensuring unitarity and connecting with worldline instanton and WKB methods for accurate probability calculations.

Contribution

It introduces a recursive perturbative expansion of the proper time propagator and links pair production probabilities to singularities, unifying various computational techniques.

Findings

Unambiguous unitarity in pair production via real proper time formulation.

Agreement of local constant approximation with worldline instanton results.

Connection of WKB cycles and Lefschetz thimbles to pair production probabilities.

Abstract

The pair production of scalar particles in electromagnetic background fields is analyzed using real proper time formulation of 1-loop effective action. After explaining how real proper time formulation keeps unitarity of the particle creation process in an unambiguous way and discussing the (lack of) pair production in uniform (magnetic) electric backgrounds, we apply these ideas to general electric field backgrounds. Our approach is based on a recursive perturbative expansion of the proper time propagator $U(t)$ and we show how the pair production probabilities can be obtained from its singularities which arises upon a Pade summation of the expansion. We computed the pair production probabilities for general space or time dependent electric fields in locally constant approximation and showed they match with the well-known worldline instanton calculations of pulse and periodic backgrounds. Later, for one dimensional periodic electric and magnetic backgrounds, we showed how the WKB integrals appear in the classical limit. We linked both cases to specific WKB cycles in different spectral regions of the WKB problem and computed the WKB actions by evaluating the WKB integrals as well as by taking phase space integrals directly along Lefschetz thimbles. Finally, we explain the equivalence of our construction with exact WKB method in the classical limit by showing how the WKB cycles precisely contribute to the pair production process which is in complete agreement with our time dependent setting.