  We rewrite the imaginary-time formalism of finite temperature field theory in
a form that all graphs used in calculating physical processes do not have any
loops. Any production of a particle from a heat bath which is itself not
thermalized or the decay and absorption of a similar particle in the bath is
expressed entirely in terms of the sum of particle interaction processes. These
are themselves very general in meaning. They can be straight forward
interactions or the more subtle and less well-known purely interference
processes that do not have a counter part in the vacuum.
