Canonical Formulation of a New Action for a Non-relativistic Particle Coupled to Gravity
arXiv:1910.01452 · doi:10.1103/PhysRevD.101.126013
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.
arXiv comment15 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 (11)
- General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
- Newtonian Gravity and the Bargmann Algebra
- On the coupling of Galilean-invariant field theories to curved spacetime
- Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
- A new formulation of non-relativistic diffeomorphism invariance
- Standard and Generalized Newtonian Gravities as ``Gauge'' Theories of the Extended Galilei Group - I: The Standard Theory
- New approach to nonrelativistic diffeomorphism invariance and its applications
- Torsional Newton-Cartan geometry from Galilean gauge theory
- 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