Chumachenko A. Long-wave asymptotics of the Green’s functions and infrared divergencies in the microscopic theory of superfluidity of Bose liquid 4He

This thesis concerns the problem of the infrared divergences which appears in the microscopic field theory of strongly interacting Bose system. This calls for a systematic renormalization, which has been performed recently by Pistoleci F., Castellani C., Di Kastro C., Strinati G. In this thesis were shown that the essential results of this procedure are equivalent to obtained using the Popov’s hydrodynamic approach modified for the case of strongly interacting Bose system. This shows that Popov’s approach correctly identifies the infrared fixed point of the renormalized effective action.Using the modified Popov’s approach the infrared asymptotic of single particle hydrodynamic, normal and anomalous Green’s functions were calculated. The modified hydrodynamic formalism was applied in order to find expressions for the density-density response as well as the density-current response, which are infrared finite. Obtained expressions are in agreement with the results obtained by Gavoret J. and Nozieres P.The quasi-particle density for T >> c|q| and T << c|q| was also calculated. Obtained formulas agrees with results obtained by Giorgini S., Pitaevskii L. and Stringari S. In this thesis this residual interaction were used in order to calculate the quasiparticle decay at small energy and momenta in second order perturbation theory. In the low density limit obtained expressions agrees with Popov’s result and at zero temperature it coincide with Beliaev’s result.As it was shown by Popov calculation of high order diagrams can be reduced to the solution of the kinetic type equations. Using this method the temperature corrections for the velocities of the first and second sounds for strongly correlated Bose system was calculates.Using the results of modified Popov theory and the model proposed by E.Pashitskii and S.Vilchinskyy the temperature dependence of the density of superfluid component of Bose liquid 4He was calculated.