Journal of Statistical Physics, Vol. 80, Nos. 3/4, 1995. p. 875-918.
It is demonstrated that the thermal structure of the noncritical free Bose gas is completely described by certain periodic generalized Gaussian stochastic process or equivalently by a certain periodic generalized Gaussian random field. Elementary properties of this Gaussian stochastic thermal structure are established.
Gentle perturbations of several types of the free thermal stochastic structure are studied. In particular, new models of non-Gaussian thermal structures are constructed and a new functional integral representation of the corresponding Euclidean-time Green functions is obtained rigorously.