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.