Axiomatic Analyticity Properties and Representations of Particles in Thermal Quantum Field Theory

We provide an axiomatic framework for Quantum Field Theory at finite temperature which implies the existence of general analyticity properties of the $n$-point functions; the latter parallel the properties derived from the usual Wightman axioms in the vacuum representation of Quantum Field Theory. Complete results are given for the propagators, including a generalization of the K\"all\'en-Lehmann representation. Some known examples of ``hard-thermal-loop calculations'' and the representation of ``quasiparticles'' are discussed in this general framework.