Finite-Temperature Instantons from First Principles

TL;DR

This paper derives the finite-temperature quantum tunneling rate from first principles, showing it involves both real and imaginary time and is best described using a Schwinger-Keldysh contour, with implications for high- and low-temperature regimes.

Contribution

It introduces a first-principles derivation of finite-temperature instantons using a Schwinger-Keldysh contour, extending previous results to general initial states and background fields.

Findings

Instantons are defined on a Schwinger-Keldysh contour.

The Euclidean-time result emerges in the large-time limit.

The scheme accounts for large finite-temperature effects.

Abstract

We derive the finite-temperature quantum-tunneling rate from first principles. The rate depends on both real- and imaginary-time; we demonstrate that the relevant instantons should therefore be defined on a Schwinger-Keldysh contour, and how the familiar Euclidean-time result arises from it in the limit of large physical times. We generalize previous results for general initial states, and identify distinct behavior in the high- and low-temperature limits, incorporating effects from background fields. We construct a consistent perturbative scheme that incorporates large finite-temperature effects.