Thermal Green Functions in Coordinate Space for Massless Particles of any Spin

The thermal Wightman functions for free, massless particles of spin 0, 1/2, 1, 3/2, and 2 are computed directly in coordinate space by solving the appropriate differential equation and imposing the Kubo-Martin-Schwinger condition. The solutions are valid for real, imaginary, or complex time. The Wightman functions for spin 1 gauge bosons and for spin 2 gravitons are directly related to the fundamental functions for spin 0. The Wightman functions for spin 3/2 gravitinos is directly related to that for spin 1/2 fermions. Calculations for spin 1, 3/2, and 2 are done in covariant gauges. In the deep space-like region the Wightman functions for bosons fall like $T/r$ whereas those for the fermions fall exponentially. In the deep time-like region all the Wightman functions fall exponentially.Comment: 8 pages, RevTex twocolum

Finite-temperature Feynman propagator in operator form

In momentum space the time-ordered, retarded, and Feynman thermal propagators all satisfy rather simple dispersion relations. In coordinate space the first two propagators are related to the thermal Wightman function Tr[{phi}({ital x}){phi}(0){ital e}{sup {minus}{beta}{ital H}}]. However, the Feynman thermal propagator in coordinate space, {ital D}{sub {ital F}}({ital x}), is not related to this thermal average and does not satisfy a KMS condition in complex time. When expressed in terms of matrix elements of the field operator, it requires a new type of operator ordering. {copyright} {ital 1996 The American Physical Society.