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We develop a new method that allows us to map models of interacting fermionsonto bosonic models describing collective excitations in an arbitrarydimension. This mapping becomes exact in the thermodynamic continuous timelimit. The boson models can be written either in the form of a model ofnon-interacting bosons in a fluctuating auxiliary field or in the form of asuperfield theory of interacting bosons. We show how one can study the latterversion using perturbation theory. Using the developed diagrammatic techniquewe compared the first two orders of perturbation theory with the correspondingresults for the original fermion model and found a perfect agreement. Asconcerns the former representation, we suggest a scheme that may be suitablefor Monte Carlo simulations and demonstrate that it is free of the fermionicsign problem. We discuss in details the properties of the bosonicrepresentation and argue that there should not be any obstacles preventing froman efficient computation.

Describing systems of interacting fermions by boson models: exact mapping in arbitrary dimension and applications