PATH-INTEGRALS FOR THE NONRELATIVISTIC ELECTRON INTERACTING WITH THE BLACK-BODY RADIATION

Feynman's method to write the polaron free energy as a functional inte gral is extended to the electron coupled to the radiation field at fin ite temperature. To actually perform the summation over the Boson degr ees of freedom, we use a path-ordered version of the Feynman-Kac-Ito f ormula. Like in the polaron case, the resulting free energy derives fr om an action involving a double stochastic integral with respect to th e tied-down Brownian motion. This representation is sufficiently expli cit to allow us to take first steps towards solving the renormalizatio n problem (removal of the high-energy cutoff). To order e(2), the reno rmalized free energy is determined and is seen to behave like T-2 at s mall temperatures. The thermodynamical effects, although very small in any laboratory, may become considerable when studying end products of stellar evolution such as white dwarfs and neutron stars. (C) 1995 Ac ademic Press, Inc.