Canonical quantization of motion on submanifolds

Abstract

This is an extended version of the talk given by the Author at the 40th Symposium on Mathematical Physics held in Torun, Poland, June 25-28, 2008. We review the methods of canonical quantization of free particle motion on curved submanifolds considered as a system with second class constraints. The work is based on our previous articles, quant-ph/0508044 and quant-ph/0508111. However, some new results are also presented.

19 pages; 40th Symposium on Mathematical Physics held in Torun, Poland, June 25-28, 2008; in v.2 some references added

References in corpus (5)

• Quantum graphs as holonomic constraints
• Constraint-induced mean curvature dependence of Cartesian momentum operators
• Wave functions in the neighborhood of a toroidal surface; hard vs. soft constraint
• Thin layer quantization in higher dimensions and codimensions
• Dirac quantization of free motion on curved surfaces

Cited by in corpus (13)

• Geometric Momentum: the Proper Momentum for a Free Particle on a Two-dimensional Sphere
• Can the canonical quantization be accomplished within the intrinsic geometry?
• Geometric momentum for a particle constrained on a curved hypersurface
• Geometric Potential Resulting from Dirac Quantization
• Geometric scattering of a scalar particle moving on a curved surface in the presence of point defects
• Dirac Equation on a Curved 2+1 Dimensional Hypersurface
• Scattering due to geometry: The case of a spinless particle moving on an asymptotically flat embedded surface
• An inhomogeneous toy-model of the quantum gravity with explicitly evolvable observables
• Hamiltonian and Lagrangian BRST quantization in Riemann Manifold
• Hamiltonian and Lagrangian BRST quantization in Riemann Manifold II
• Geometric scattering in the presence of line defects
• Quantum Mechanics on Curved Hypersurfaces
• Extrinsic curvature effects in brane-world scenarios