The imaginary time Path Integral and non-time-reversal-invariant- saddle points of the Euclidean Action

TL;DR

This paper introduces boomerons, new non-time-reversal-invariant solutions to Euclidean equations of motion, which impact vacuum energy calculations and suggest a novel way to address fake vacuum instabilities in quantum theories.

Contribution

It presents the concept of boomerons, expanding the set of solutions in Euclidean path integrals and exploring their role in vacuum stability and cancellation mechanisms.

Findings

Boomerons are new bounce-like solutions affecting vacuum energy.

Cancellation of boomeron contributions can remove fake vacuum instabilities.

Sign choices in the path integral influence the contribution of boomerons.

Abstract

We discuss new bounce-like (but non-time-reversal-invariant-) solutions to Euclidean equations of motion, which we dub boomerons. In the Euclidean path integral approach to quantum theories, boomerons make an imaginary contribution to the vacuum energy. The fake vacuum instabilty can be removed by cancelling boomeron contributions against contributions from time reversed boomerons (anti-boomerons). The cancellation rests on a sign choice whose significance is not completely understood in the path integral method.