A generalized Noether theorem for scaling symmetry

Abstract

The recently discovered conserved quantity associated with Kepler rescaling is generalised by an extension of Noether's theorem which involves the classical action integral as an additional term. For a free particle the familiar Schroedinger dilations are recovered. A general pattern arises for homogeneous potentials. The associated conserved quantity allows us to derive the virial theorem. The relation to the Bargmann framework is explained and illustrated by exact plane gravitational waves.

affiliation corrected

References in corpus (14)

• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• Phenomenology of local scale invariance: from conformal invariance to dynamical scaling
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Local scale invariance and strongly anisotropic equilibrium critical systems
• Carroll symmetry of plane gravitational waves
• Screw-symmetric gravitational waves: a double copy of the vortex
• Velocity Memory Effect for Polarized Gravitational Waves
• Scaling and conformal symmetries for plane gravitational waves
• Memory effect, conformal symmetry and gravitational plane waves
• Gravitational Waves: Just Plane Symmetry
• Null lifts and projective dynamics
• "Kepler Harmonies" and conformal symmetries
• Integrability of geodesic motions in curved manifolds through non-local conserved charges
• A Note on the scale symmetry and Noether current

Cited by in corpus (11)

• Near horizon dynamics of three dimensional black holes
• Scaling and conformal symmetries for plane gravitational waves
• Conformal symmetries and integrals of the motion in pp waves with external electromagnetic fields
• Extension of Noether's theorem in PT-symmetric systems and its experimental demonstration in an optical setup
• "Kepler Harmonies" and conformal symmetries
• A note on broken dilatation symmetry in planar noncommutative theory
• Generalized dilaton gravity in 2d
• Cartan Connection for Schrödinger equation. The nature of vacuum
• Relative Equilibria for Scaling Symmetries and Central Configurations
• Generation of new symmetries from explicit symmetry breaking
• Circularly polarized periodic gravitational wave and the Pais-Uhlenbeck oscillator