On the hydrodynamic canonical formalism of the Gross-Pitaevskii field

TL;DR

This paper develops a canonical formalism for the hydrodynamic representation of the Gross-Pitaevskii field, treating the condensate's density and phase as conjugate variables using advanced Lagrangian methods.

Contribution

It introduces a novel canonical formalism for the Gross-Pitaevskii field's hydrodynamics, employing Dirac-Bergmann and Faddeev-Jackiw techniques.

Findings

Faddeev-Jackiw method is more direct for this formalism

Established conjugate variables as density and phase

Provides a new framework for hydrodynamic Gross-Pitaevskii analysis

Abstract

We derive a canonical formalism for the hydrodynamic representation of the Gross-Pitaevskii field (nonlinear Schr\"odinger field), where the density and the phase of the condensate form a canonical pair of conjugate field variables. To do so, we treat the meanfield as a singular Lagrangian system and apply both the Dirac-Bergmann and Faddeev-Jackiw methods. The Faddeev-Jackiw method is found to be a more direct approach to the problem.