Crossing singularities in the saddle point approximation

TL;DR

This paper uncovers a universal phenomenon where complex classical paths in real-time path integrals encounter singularities, requiring analytic continuation, which is crucial for understanding quantum tunneling.

Contribution

It introduces the concept of paths hitting potential singularities and demonstrates their importance in the analysis of quantum tunneling within real-time path integrals.

Findings

Complex paths hit potential singularities during analytic continuation

Universal behavior observed in the crossing of singularities

Enrichment of real-time Feynman path integral analysis

Abstract

We describe a new phenomenon in the study of the real-time path integral, where complex classical paths hit singularities of the potential and need to be analytically continued beyond the space for which they solve the boundary value problem. We show that the behavior is universal and central to the problem of quantum tunneling. These analytically continued complex classical paths enrich the study of real-time Feynman path integrals.