Perfect fluid equations with N=1,2 Schrodinger supersymmetry

Abstract

Superconformal extensions of the perfect fluid equations, which realize $N=1,2$ Schrodinger superalgebra, are constructed within the Hamiltonian formalism. They are built by introducing real (for $N=1$) or complex (for $N=2$) anticommuting field variables as superpartners for the density and velocity of a fluid. The full set of conserved charges associated with the $N=1,2$ Schrodinger superalgebra is constructed. Within the Lagrangian formalism, when the Clebsch decomposition for the velocity vector field is used, the anticommuting variables can be interpreted as potentials parameterizing fluid's vorticity.

1+15 pages; v2: appendix, comments and references added, typos corrected

References in corpus (10)

• Gravity duals for non-relativistic CFTs
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Remark on quantum mechanics with N=2 Schrodinger supersymmetry
• Schrödinger symmetry: a historical review
• The group-theoretic approach to perfect fluid equations with conformal symmetry
• Equations of fluid dynamics with the l-conformal Galilei symmetry
• On non-equilibrium physics and string theory
• Hamiltonian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• Lagrangian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• Perfect fluid dynamics with conformal Newton-Hooke symmetries