  P representation techniques, which have been very successful in quantum
optics and in other fields, are also useful for general bosonic quantum
dynamical many-body calculations such as Bose-Einstein condensation. We
introduce a representation called the gauge P representation which greatly
widens the range of tractable problems. Our treatment results in an infinite
set of possible time-evolution equations, depending on arbitrary gauge
functions that can be optimized for a given quantum system. In some cases,
previous methods can give erroneous results, due to the usual assumption of
vanishing boundary conditions being invalid for those particular systems.
Solutions are given to this boundary-term problem for all the cases where it is
known to occur: two-photon absorption and the single-mode laser. We also
provide some brief guidelines on how to apply the stochastic gauge method to
other systems in general, quantify the freedom of choice in the resulting
equations, and make a comparison to related recent developments.
