The positivity of the Boltzmann weight, needed for its probabilistic interpretation and for the application of the Monte Carlo method is absent for theories with complex actions. We propose avoiding the latter problem substituting Monte Carlo simulations by computations with convergent 'non-perturbative' expansions. We discuss constructions of such expansions and first numerical results on the examples of $phi^4$-model at zero/non-zero chemical potential and lattice QED.

Theoretical Developments