Canonical Formulation of a New Action for a Non-relativistic Particle Coupled to Gravity

Abstract

A detailed canonical treatment of a new action for a nonrelativistic particle coupled to background gravity, recently given by us, is performed both in the Lagrangian and Hamiltonian formulations. The equation of motion is shown to satisfy the geodesic equation in the Newton-Cartan background, thereby clearing certain confusions. The Hamiltonian analysis is done in the gauge independent as well as gauge fixed approaches, following Dirac's analysis of constraints. The physical (canonical) variables are identified and the path to canonical quantisation is outlined by explicitly deriving the Schroedinger equation.

15 pages, latex, reference to the text are increased, no new reference added 15 pages, Latex, presentation slightly revised. This version to appear in Physical Review D

References in corpus (6)

• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Newtonian Gravity and the Bargmann Algebra
• A new formulation of non-relativistic diffeomorphism invariance
• General algorithm for non-relativistic diffeomorphism invariance
• Non-relativistic Spinning Particle in a Newton-Cartan Background
• A New Action for Nonrelativistic Particle in Curved Background

Cited by in corpus (5)

• Non-relativistic transport from frame-indifferent kinetic theory
• Covariant Formulation of the Newton-Hooke Particle and its Canonical Analysis
• Canonical Formulation for a Non-relativistic Spinning Particle Coupled to Gravity
• Geometry of Nonrelativistic string
• Hamiltonian analysis of the Schroedinger field coupled with dynamic non-relativistic gravity