The existence of positive representations for complex weights

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 can be represented by real and positive weights p ( z ) on , 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.