Beyond complex Langevin equations I: two simple examples

Abstract

By introducing a second complex variable, the integral relation between a complex density and the corresponding positive distribution is derived. Together with the positivity and normalizability conditions, this sum rule allows to construct explicitly equivalent pairs of distributions in simple cases discussed here. In particular the well known solution for a complex gaussian distribution is generalized to an arbitrary complex inverse dispersion parameter. This opens a possibility of positive representation of Feynman path integrals directly in the Minkowski time.

References added

References in corpus (1)

• Heavy dense QCD from a 3d effective lattice theory

Cited by in corpus (3)

• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Does the complex Langevin method give unbiased results?
• Beyond Complex Langevin Equations: a Progress Report