Beyond Complex Langevin Equations: positive representation of a class of complex measures

Erhard Seiler; Jacek Wosiek

doi:10.1051/epjconf/201817511004

EPJ

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Proceedings

Open Access

EPJ Web of Conferences 175, 11004 (2018)
https://doi.org/10.1051/epjconf/201817511004

Beyond Complex Langevin Equations: positive representation of a class of complex measures

Erhard Seiler¹ and Jacek Wosiek²^*^,**

¹ Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München, Germany
² M. Smoluchowski Institute of Physics, Jagiellonian University, Cracow, Poland

^* Speaker, e-mail: Jacek.Wosiek@uj.edu.pl

Published online: 26 March 2018

Abstract

A positive representation for a set of complex densities is constructed. In particular, complex measures on a direct product of U(1) groups are studied. After identifying general conditions which such representations should satisfy, several concrete realizations are proposed. Their utility is illustrated in few concrete examples representing problems in abelian lattice gauge theories.

^**

Acknowledges financial support by the NCN grant UMO-2016/21/B/ST2/01492

© The Authors, published by EDP Sciences, 2018

This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).