The group-theoretic approach to perfect fluid equations with conformal symmetry

TL;DR

This paper explores how the nonlinear realizations method can be used to derive perfect fluid equations exhibiting conformal symmetry, analyzing four specific symmetry groups to understand its strengths and limitations.

Contribution

It applies the nonlinear realizations approach to construct perfect fluid equations with various conformal symmetries, highlighting its advantages and constraints.

Findings

Successfully derived fluid equations for four symmetry groups

Identified specific advantages of the nonlinear realizations method

Discussed limitations and potential improvements

Abstract

The method of nonlinear realizations is a convenient tool for building dynamical realizations of a Lie group, which relies solely upon structure relations of the corresponding Lie algebra. The goal of this work is to discuss advantages and limitations of the method, which is here applied to construct perfect fluid equations with conformal symmetry. Four cases are studied in detail, which include the Schrodinger group, the l-conformal Galilei group, the Lifshitz group, and the relativistic conformal group.