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

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.Comment: 19 pages, LaTex, 5 epsf figures. A new example from quantum mechanics is included. The role of internal symmetries is discussed. To be published in Nucl. Phys.