Goldstone Boson Normal Coordinates in Interacting Bose Gases

TL;DR

This paper explicitly constructs Goldstone Boson fluctuation operators in interacting Bose gases, showing their canonical nature, relation to symmetry breaking, and dynamic behavior, with implications for long-wavelength spectrum analysis.

Contribution

It provides an explicit construction of Goldstone Boson fluctuation operators as canonical pairs in interacting Bose gases, linking them to symmetry breaking and dynamic properties.

Findings

Canonical pair of fluctuation operators related to order parameter and symmetry generator

One operator exhibits anomalous behavior, the other is squeezed

Long wavelength spectrum influences the lifetime of the pair

Abstract

For the phenomenon of Bose-Einstein condensation we construct the canonical pair of field operators of the Goldstone Bosons explicitly as fluctuation operators in the ground state. We consider the imperfect Bose gas as well as the weakly interacting Bose gas. We prove that a canonical pair of fluctuation operators is always related to the order parameter and the generator of the broken symmetry fluctuations. We find that although the first one has an anomalous behaviour, the second one is squeezed by the same inverse rate. Furthermore, we prove that this canonical pair separates from the other variables of the system and that it behaves dynamically as oscillator variables. Finally the long wavelength behaviour of the spectrum determines the lifetime of this pair.