Abstract
The modular structure of the free Bose gas is completely described by a Gaussian periodic OS-positive generalized Markov process with values in S′(Rd). Methods of Euclidean quantum field theory are applied to study some Gibbsian perturbations of the corresponding free Bose gas stochastic thermal structures leading to constructions of some modular structures which describe interacting Bosons in the thermal equilibrium. In particular it is shown that certain perturbations of the free Bose gas in the critical regime of couplings preserve nonergodicity and this phenomenon seems to be connected to the preservation of the Bose-Einstein condensate in the interacting system.
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