The paper deals the mathematical model of weakly coupled high degenerate qu
antum fluid. We try to calculate the thermodynamical properties of state fo
r the Lennard-Jones fluid with help of quantum field theory of many particl
e systems and finite temperature formalism. We used Feynman-Dyson perturbat
ion theory. We developed an expression for the grand potential with help of
temperature Green functions and Feynman diagrams. The results of the analy
sis are compared with experimental data and other models and shout a relati
vely good agreement. This model is the first experiment for calculating the
thermodynamical functions of refrigerants at temperatures T>>0K.