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

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