  The Feynman-Vernon formalism is used to obtain a microscopic, quantum
mechanical derivation of black body radiation, for a massless scalar field in
1+1 dimensions, weakly coupled to an environment of finite size. The model
exhibits the absorption, thermal equilibrium, and emission properties of a
canonical black body, but shows that the thermal radiation propagates outwards
from the body, with the Planckian spectrum applying inside a wavefront region
of finite thickness. The black body environment used in the derivation can be
considered to represent a very fine, granular medium, such as lampblack. In the
course of developing the model for black body radiation, thermalization of a
single harmonic oscillator by a heat bath with slowly varying spectral density
is demonstrated. Bargmann-Fock coherent state variables, being convenient for
problems involving harmonic oscillators and free fields, are reviewed and then
used throughout the paper. An appendix reviews the justification for using
baths of independent harmonic oscillators to model generic quantum
environments.
