Field-dependent symmetries of a non-relativistic fluid model

TL;DR

This paper explores the unique field-dependent symmetries of a non-relativistic fluid model, revealing their connection to Poincaré and conformal groups through a Kaluza-Klein framework, and deriving related conserved quantities.

Contribution

It demonstrates how a non-relativistic fluid model exhibits field-dependent symmetries linked to Poincaré and conformal groups using a Kaluza-Klein approach.

Findings

Symmetries include Poincaré and conformal groups.

Conserved quantities are derived from these symmetries.

Symmetry extension occurs in the non-interacting case.

Abstract

As found by Bordemann and Hoppe and by Jevicki, a certain non-relativistic model of an irrotational and isentropic fluid, related to membranes and to partons, admits a Poincar\'e symmetry. Bazeia and Jackiw associate this dynamical symmetry to a novel type of ``field dependent'' action on space-time. The ``Kaluza-Klein type'' framework of Duval et al. is used to explain the origin of these symmetries and to derive the associated conserved quantities. In the non-interacting case, the symmetry extends to the entire conformal group.