In quantum field theory, heavy particles with mass M much greater than the
temperature T give not only effects suppressed by the Boltzmann factor c(-M
/T), but also effects suppressed by powers of T/M. We show that power-suppr
essed terms in equilibrium observables arise from effective interactions am
ong light particles due to virtual heavy particles. We study a model introd
uced by Matsumoto and Yoshimura in which heavy bosons interact only through
a term that allows pair annihilation into light particles. We construct an
effective Lagrangian fur the light held by integrating out the heavy field
, and use it to calculate the leading power-suppressed terms in the energy
density. The thermal average of the Hamiltonian density for the heavy field
includes a term proportional to T-6/M-2, but we show that this term can he
eliminated by a field redefinition and therefore cannot have any physical
significance.