New Geometric Transition as Origin of Particle Production in Time-Dependent Backgrounds

TL;DR

This paper introduces a geometric transition framework in complex time to explain particle production in dynamic backgrounds, linking multi-pair creation to topological features like winding numbers.

Contribution

It extends quantum evolution analysis into complex time, revealing geometric transitions as the origin of particle production in various backgrounds.

Findings

Particle production depends on the winding number of the complex-time path.

The geometric transition approach applies to Schwinger and Gibbons-Hawking mechanisms.

Multi-pair production is governed by topological properties of the evolution path.

Abstract

By extending the quantum evolution of a scalar field in time-dependent backgrounds to the complex-time plane and transporting the in-vacuum along a closed path, we argue that the geometric transition from the simple pole at infinity determines the multi-pair production depending on the winding number. We apply the geometric transition to Schwinger mechanism in the time-dependent vector potential for a constant electric field and to Gibbons-Hawking particle production in the planar coordinates of a de Sitter space.