Relativistic KMS-condition and Kaellen-Lehmann type representatios of thermal propagators

A relativistic version of the Kubo--Martin--Schwinger boundary condition is presented which fixes the properties of thermal equilibrium states with respect to arbitrary space--time translations. This novel condition is a natural generalization of the relativistic spectrum condition in the vacuum theory and has similar consequences. In combination with the condition of locality it gives rise to a Kaellen--Lehmann type representation of thermal propagators with specific regularity properties. Possible applications of the results and some open problems are outlined.