Positive Representations of a Class of Complex Measures

Abstract

We study the problem of constructing positive representations of complex measures. In this paper we consider complex densities on a direct product of $U(1)$ groups and look for representations by probability distributions on the complexification of those groups. After identifying general necessary and sufficient conditions we propose several concrete realizations. Finally we study some of those realizations in examples representing problems in abelian lattice gauge theories.

19 pages, 3 figures, minor changes to bring it into agreement with published version

References in corpus (7)

• Lattice simulations of real-time quantum fields
• Stochastic quantization at finite chemical potential
• Lattice Simulations of the Thermodynamics of Strongly Interacting Elementary Particles and the Exploration of New Phases of Matter in Relativistic Heavy Ion Collisions
• Complex Langevin dynamics and zeroes of the fermion determinant
• Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion
• Does the complex Langevin method give unbiased results?
• Existence of positive representations for complex weights

Cited by in corpus (5)

• Review on novel methods for lattice gauge theories
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Towards learning optimized kernels for complex Langevin
• Positive representations of complex distributions on groups
• Necessary and sufficient conditions for correctness of complex Langevin