Impurity self-energy in the strongly-correlated Bose systems

We proposed the nonperturbative scheme for the calculation of the impurity spectrum in the Bose system at zero temperature. The method is based on the path-integral formulation and describes an impurity as a zero-density ideal Fermi gas interacting with Bose system for which the action is written in terms of density fluctuations. On the example of the 3He atom immersed in the liquid helium-4 a good consistency with experimental data and results of Monte Carlo simulations is shown.