The He II Theory Preserving the Symmetry of the Initial Hamiltonian of the System

Abstract

The article suggests a method for the construction of the number of atoms preserving microscopic He II theory. The suggested theory can provide the ground state wave function (WF) as an expansion in series by small parameters. In addition, errors in the definition of the WFs of the excited states turn out to be vanishingly small while the system size increases. Predictions of the proposed theory and of the Bogoliubov theory are identical if helium occupies a simply connected volume. However, there are differences in the general case. These differences are due to the fact that the operator of the occupation number of the zero momentum state does not commute with the creation and annihilation operators of phonons. This contradicts the Bogoliubov assumption that the creation and annihilation operators of atoms in the zero momentum state can be replaced by a c-number. The latter, as is known, should commute with any operator. This should lead to a difference in the results of calculation of helium flow through the tunnel transition. Therefore, the suggested theory is not equivalent to Bogoliubov theory.