Representation of coherent states in the theory of many-boson systems

A solution of the Bloch equation for the density matrix of a system of interacting Bose particles is found in the representation of coherent states. The matrix of the functional of the thermodynamic potential is represented by a functional series in eigenvalues of the annihilation operator, and the coefficient functions are matrix elements of the cluster operators. A simple functional integration in the partition function leads to the well-known quantum viriaI expansions and the standard perturbation theory series. The possibility of applying the expressions obtained here to the investigation of the $\lambda$-transition in liquid $\operatorname{He}^4$, and also their generalization to the case of a many-fermion system is discussed.