  The general idea of a stochastic gauge representation is introduced and
compared with more traditional phase-space expansions, like the Wigner
expansion. Stochastic gauges can be used to obtain an infinite class of
positive-definite stochastic time-evolution equations, equivalent to master
equations, for many systems including quantum time-evolution. The method is
illustrated with a variety of simple examples ranging from astrophysical
molecular hydrogen production, through to the topical problem of Bose-Einstein
condensation in an optical trap and the resulting quantum dynamics.
