Local properties of equilibrium states and the particle spectrum in quantum field theory (Q1081092)

This work is a test of the first author's conjecture according to which the nuclearity of the essentially localized states in a local quantum field theory is a physically pertinent criterium to select models with a reasonable thermodynamic behaviour. In the case of the class of models with a countable number of free scalar particles with masses \(m_ i\), \(i\in {\mathbb{N}}\), this criterium is equivalent to the finiteness of the sum \(\sum^{\infty}_{i=1}e^{- \beta m_ i}\) for any \(\beta >0\). The authors show that this last condition is in turn equivalent, for these models, to the existence of locally normal equilibrium states with finite energy density for all temperatures \(\beta >0\).