Quantum dynamics of non-relativistic particles and isometric embeddings

Abstract

It is considered, in the framework of constrained systems, the quantum dynamics of non-relativistic particles moving on a d-dimensional Riemannian manifold M isometrically embedded in $R^{d+n}$. This generalizes recent investigations where M has been assumed to be a hypersurface of $R^{d+1}$. We show, contrary to recent claims, that constrained systems theory does not contribute to the elimination of the ambiguities present in the canonical and path integral formulations of the problem. These discrepancies with recent works are discussed.

Revtex, 14 pages

References in corpus (4)

• Quantization of systems with time-dependent constraints. Example of relativistic particle in plane wave
• On the definition of Quantum Free Particle on Curved Manifolds
• Nonrelativistic Quantum Particle in a Curved Space as a Constrained System
• Canonical quantization of the relativistic particle in static spacetimes

Cited by in corpus (8)

• A Geometric Formulation of Quantum Stress Fields
• Quantization of Point-Like Particles and Consistent Relativistic Quantum Mechanics
• How the Geometric Calculus Resolves the Ordering Ambiguity of Quantum Theory in Curved Space
• Hamilton-Jacobi treatment of a non-relativistic particle on a curved space
• Quantization of spinning particle in arbitrary background
• Covariant quantizations in plane and curved spaces
• Hamiltonian and Lagrangian BRST quantization in Riemann Manifold
• Hamiltonian and Lagrangian BRST quantization in Riemann Manifold II