Gentle Perturbations of the Free Bose Gas I

TL;DR

This paper characterizes the thermal structure of the noncritical free Bose Gas using Gaussian stochastic processes, introduces gentle perturbations, and constructs new non-Gaussian models with rigorous functional integral representations.

Contribution

It provides a comprehensive Gaussian description of the free Bose Gas's thermal structure and introduces novel non-Gaussian models with rigorous mathematical foundations.

Findings

Thermal structure described by periodic Gaussian processes.

Construction of new non-Gaussian thermal models.

Rigorous functional integral representation of Green functions.

Abstract

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 certain periodic generalized Gaussian random field. Elementary properties of this Gaussian stochastic thermal structure have been established. Gentle perturbations of several types of the free thermal stochastic structure are studied. In particular new models of non-Gaussian thermal structures have been constructed and a new functional integral representation of the corresponding euclidean-time Green functions have been obtained rigorously.