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

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

2000-07-13

arxiv.org/abs/hep-ph/0007138v1

Phys.Rev. D62 (2000) 056010

Physics

High Energy Physics

High Energy Physics - Phenomenology

8 pages, RevTex twocolumn

Scientific paper

10.1103/PhysRevD.62.056010

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.

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