Complex-time path-integral formalism for quantum tunneling

TL;DR

This paper introduces a complex-time path-integral formalism for quantum tunneling, providing a method to accurately derive WKB results by incorporating instantons and boundary conditions.

Contribution

It develops a reduction formula within the complex-time path-integral framework that correctly reproduces WKB results for quantum tunneling, overcoming limitations of saddle-point approximations.

Findings

Subleading complex-time saddle-points do not yield correct WKB results.

The reduction formula allows construction of Green functions from simple potential components.

The method successfully incorporates instantons, bounces, and boundary conditions in tunneling analysis.

Abstract

The complex-time formalism is developed in the framework of the path-integral formalism, to be used for analysis of the quantum tunneling phenomena. We show that subleading complex-time saddle-points do not account for the right WKB result. Instead, we develop a reduction formula, which enables us to construct Green functions from simple components of the potential, for which saddle-point method is applicable. This method leads us to the valid WKB result, which incorporates imaginary-time instantons and bounces, as well as the real-time boundary conditions.