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We present a novel norm preserving stochastic evolution equation for a Bosefield. Ensemble averages are quantum expectation values in the canonicalensemble. This numerically very stable equation suppresses high-energyfluctuations exponentially, preventing cutoff problems to occur. We present 3Dsimulations for an ideal gas in various trapping potentials focussing on groundstate occupation numbers and spatial correlation functions for a wide range oftemperatures above and below the critical temperature. Although rigorouslyvalid for non-interacting Bosons only, we argue that weakly interacting Bosegases may also be amenable to this approach, in the usual mean-fieldapproximation.

Stochastic field equation for the canonical ensemble of a Bose gas