Beyond Complex Langevin Equations: a Progress Report

TL;DR

This paper reviews recent advances in avoiding complex stochastic processes in Complex Langevin methods, enabling the construction of positive, normalizable representations for Minkowski-time quantum path integrals, with connections to thimble approaches.

Contribution

It introduces new developments that allow direct construction of positive, normalizable representations for Minkowski-time quantum path integrals, advancing the field beyond traditional Complex Langevin equations.

Findings

Constructed positive, normalizable representations for Minkowski path integrals.

Linked the new methods to thimble approaches.

Reported progress in complex stochastic process avoidance.

Abstract

After a short review of one of proposals to avoid complex stochastic processes in Complex Langevin studies, the recent progress in the former is reported. In particular, the new developments allow now to construct positive and normalizable representations for gaussian quantum mechanical, as well as field theoretical, path integrals directly in the Minkowski time. A relation to the idea of thimbles is also discussed.