  We present phase-space techniques for the modelling of spontaneous emission
in two-level bosonic atoms. The positive-P representation is shown to give a
full and complete description and can be further developed to give exact
treatments of the interaction of degenerate bosons with the electromagnetic
field in a given experimental situation. The Wigner representation, even when
truncated at second order, is shown to need a doubling of the phase-space to
allow for a positive-definite diffusion matrix in the appropriate Fokker-Planck
equation and still fails to agree with the full quantum results of the
positive-P representation. We show that quantum statistics and correlations
between the ground and excited states affect the dynamics of the emission
process, so that it is in general non-exponential.
