Path integrals for the nonrelativistic electron interacting with the black body radiation.

Details Path integrals for the nonrelativistic electron interacting with the black body radiation. Path integrals for the nonrelativistic electron interacting with the black body radiation.

Sep 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995anphy.242..386r&link_type=abstract

Ann. Phys. (N.Y.), Vol. 242, No. 2, p. 386 - 412

Physics

1

Thermodynamics, Thermodynamics: Stellar Evolution, Thermodynamics: Neutron Stars

Scientific paper

Feynman's method to write the polaron free energy as a functional integral is extended to the electron coupled to the radiation field at finite temperature. To actually perform the summation over the boson degrees of freedom, the author uses a path-ordered version of the Feynman-Kac-Ito formula. Like in the polaron case, the resulting free energy derives from an action involving a double stochastic integral with respect to the tied-down Brownian motion. This representation is sufficiently explicit to allow us to take first steps towards solving the renormalization problem (removal of the high-energy cutoff). To order e2, the renormalized free energy is determined and is seen to behave like T2 at small 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.

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