Theory of degenerate Bose gas without anomalous averages

TL;DR

This paper develops a theory for a weakly non-ideal Bose gas without using anomalous averages, revealing a gap in the one-particle spectrum while confirming the phonon-roton spectrum in density fluctuations.

Contribution

It introduces a novel approach to Bose gas theory that avoids anomalous averages and demonstrates the existence of a gap in the excitation spectrum.

Findings

The density-density Green function pole matches Bogolybov's phonon-roton spectrum.

A gap exists in the one-particle excitation spectrum.

The gap value relates to the condensate particle density.

Abstract

Theory of a weakly non-ideal Bose gas in the canonical ensemble is developed without assumption of the C-number representation of the creation and annihilation operators with zero momentum. It is shown that the pole of the "density-density" Green function exactly coincides with the Bogolybov's phonon-roton spectrum of excitations. At the same time in the one-particle excitation spectrum a gap exists. The value of this gap is connected with the density of particles in the "condensate".