Collective variables. Correlation functions on Gaussian functionals

Canonical Bose fields are represented in terms of collective variables, and this representation is used to study the correlation functions on states described by Gaussian functionals of Bogolyubov–Zubarev type. The correlation functions are expressed in terms of integrals with respect to nuclear Gaussian measures, and the existence of thermodynamic limits is proved; correlation decoupling and nondiagonaI long-range order are studied, it is found that in a nonideal Bose gas a decay of the correlations for particles of mass $m$ occurs in the region of lengths of the order of the acoustic de Broglie wavelength.