  Many-mode interacting Bose gases (1D,2D,3D) are simulated from first
principles. The model uses a second-quantized Hamiltonian with two-particle
interactions (possibly ranged), external potential, and interactions with an
environment, with no further approximations. Simulations are of a set of
stochastic equations that in the limit of many realizations correspond exactly
to the full quantum evolution. These are obtained using the stochastic gauge
method (derived here), an extension of the positive P phase-space
representation.
  The systems investigated are: 1) Dynamics of spatial correlations in uniform
1D and 2D Bose gases after the rapid appearance of significant two-body
collisions (e.g. after entering a Feshbach resonance). 2) Dynamics of
stimulated Bose enhancement of scattered atom modes during the collision of two
Bose-Einstein condensates with a mean of 150 000 atoms. 3) Dynamics of trapped
bosons, where the size of the trap is of the same order as the range of the
interparticle potential. 4) Grand canonical thermodynamics of uniform 1D Bose
gases for a variety of temperatures and collision strengths. Observables
calculated include 1st-3rd order spatial correlation functions (including
finite separation) and momentum distributions.
  The stochastic gauge method is derived, and its application to interacting
Bose gases investigated in detail. It is found to improve simulation
effectiveness under many conditions, and to be capable of overcoming
instability and boundary term problems. Additionally, conditions under which
very generalized phase-space represntations can be used to obtain tractable
many-body simulations are analysed.
