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There exist methods to reformulate in an exact way the many-body problem ofinteracting bosons in terms of the stochastic evolution of single particle wavefunctions. For one such reformulation, the so-called simple Fock scheme, wepresent an elementary derivation, much simpler than the original one.Furthermore, we show that two other schemes, based on coherent states of thematter field rather than on Fock states, lead to an infinite statisticaluncertainty in the continuous time limit. The simple Fock scheme is therefore,up to now, the only one that was proved to lead to a convergent Monte Carlosimulation scheme at all times.Comment: Proceedings of the Laser Physics Workshop held in Bratislava, July  2002. Submitted to Laser Physic

Exact Reformulation of the Bosonic Many-Body Problem in Terms of Stochastic Wave Functions: an Elementary Derivation