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

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.

v2: 23 pages, the introductory and concluding parts extended, acknowledgement and references added

References in corpus (9)

• Nonlinear Fluid Dynamics from Gravity
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Relativistic Particle and Relativistic Fluids: Magnetic Moment and Spin-Orbit Interactions
• CFT Hydrodynamics: Symmetries, Exact Solutions and Gravity
• Schwarzian mechanics via nonlinear realizations
• Equations of fluid dynamics with the l-conformal Galilei symmetry
• Topological Terms and Diffeomorphism Anomalies in Fluid Dynamics and Sigma Models
• Dynamical realizations of the Lifshitz group

Cited by in corpus (9)

• Hamiltonian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• Gauss-Bonnet AdS planar and spherical black hole thermodynamics and holography
• Remarks on higher Schwarzians
• Lagrangian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• Various disguises of the Pais-Uhlenbeck oscillator
• Perfect fluid dynamics with conformal Newton-Hooke symmetries
• Perfect fluid coupled to a solenoidal field which enjoys the l-conformal Galilei symmetry
• Perfect fluid equations with N=1,2 Schrodinger supersymmetry
• New dynamical realizations of the Lifshitz group