Theory of a many-boson system with deformed Heisenberg algebra

We propose to consider nonlinear fluctuations in the theory of liquid $^{4}$He deforming the commutation relations between the generalized coordinates and momenta. Generalized coordinates are coefficients of density fluctuations of Bose particles. The deformation parameter takes into account the effects of three- and four-particle correlations in the behavior of a system. This parameter is defined from the experimental values of the elementary excitation spectrum and the structure factor extrapolated to $T=0$ K. The numerical estimation of the ground state energy and the Bose condensate fraction is made. The elementary excitation spectrum and the potential of interaction between the helium atoms are recovered.