Existence of positive representations for complex weights

Abstract

The necessity of computing integrals with complex weights over manifolds with a large number of dimensions, e.g., in some field theoretical settings, poses a problem for the use of Monte Carlo techniques. Here it is shown that very general complex weight functions P(x) on R^d can be represented by real and positive weights p(z) on C^d, in the sense that for any observable f, <f(x)>_P = <f(z)>_p, f(z) being the analytical extension of f(x). The construction is extended to arbitrary compact Lie groups.

9 pages, no figures. To appear in J.Phys.A

References in corpus (16)

• Lattice determination of the critical point of QCD at finite T and μ
• Lattice QCD at Finite Density -- An introductory review
• Lattice simulations of real-time quantum fields
• A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory
• Simulating nonequilibrium quantum fields with stochastic quantization techniques
• The factorization method for systems with a complex action -a test in Random Matrix Theory for finite density QCD-
• New proposal for numerical simulations of theta-vacuum like systems
• Representation of Complex Probabilities
• Complex Probabilities on R^N as Real Probabilities on C^N and an Application to Path Integrals
• Lattice QCD at finite density
• On the Segregation Phenomenon in Complex Langevin Simulation
• Global Stationary Phase and the Sign Problem
• Complex Langevin Equation and the Many-Fermion Problem
• Minimum uncertainty for antisymmetric wave functions
• Microcanonical Simulation of Complex Actions: The Wess Zumino Witten Case
• Simulations with Complex Measure

Cited by in corpus (10)

• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Complex Langevin Equations and Schwinger-Dyson Equations
• Does the complex Langevin method give unbiased results?
• Gibbs sampling of complex valued distributions
• Positive Representations of a Class of Complex Measures
• Positive representations of complex distributions on groups
• Explicit positive representation for weights on $R^d$
• Necessary and sufficient conditions for correctness of complex Langevin
• The Role of Integration Cycles in Complex Langevin Simulations
• Correctness criteria for complex Langevin