Internal energy of many-boson system with three- and four-particle direct correlations taken into account

In this paper we calculate kinetic, potential and full energy with three- and four-particle direct correlations taken into account at wide temperature region on the base of the density matrix of the interacting Bose-particles [I. O. Vakarchuk, O. I. Hryhorchak, Journ. Phys. Stud. {\bf 3}, 3005 (2009)]. In the low temperature limit the obtained expression for the full energy is equal to the wellknown expression for ground state energy in the approximation of “two sums over the wave vector.” The results of this work can be applied for the numeric calculation of the heat capacity of liquid ${}^4$He in order to check the theoretical and experimental results quantatively, especially in the $\lambda$-transition region.