Nonequivalent operator representations for Bose-condensed systems

TL;DR

This paper discusses the importance of using nonequivalent operator representations in Bose-condensed systems, introducing a composite operator framework that ensures a self-consistent, conserving, and gapless description of the system.

Contribution

It develops a self-consistent theory for Bose-condensed systems using composite operator representations, ensuring conservation laws and gapless spectra.

Findings

Bose systems with and without condensate belong to different Fock spaces.

A composite representation allows for a self-consistent description of Bose-condensed systems.

The theory guarantees a gapless particle spectrum regardless of approximation.

Abstract

The necessity of accurately taking into account the existence of nonequivalent operator representations, associated with canonical transformations, is discussed. It is demonstrated that Bose systems in the presence of the Bose-Einstein condensate and without it correspond to different Fock spaces, orthogonal to each other. A composite representation for the field operators is constructed, allowing for a self-consistent description of Bose-condensed systems. Equations of motion are derived from the given Hamiltonian, which guarantees the validity of conservation laws and thermodynamic self-consistency. At the same time, the particle spectrum, obtained either from diagonalizing this Hamiltonian or from linearizing the field-operator equations of motion, has no gap. The condition of the condensate existence assures the absence of the gap in the spectrum, irrespectively to the approximation involved. The suggested self-consistent theory is both conserving and gapless.