Gauge invariant counterparts and quantization of systems under holonomic constraints

Abstract

Systems under holonomic constraints are classified within the generalized Hamiltonian framework as second-class constraints systems. We show that each system of point particles with holonomic constraints has a hidden gauge symmetry which allows to quantize it in the original phase space as a first-class constraints system. The proposed method is illustrated with quantization of a point particle moving on an $n-1$-dimensional sphere $S^{n-1}$ as well as its field theory analog the O(n) nonlinear sigma model.

arXiv comment5 pages REVTeX, new references added

References in corpus (3)

• Hamilton-Jacobi approach to Berezinian singular systems
• Multi Hamilton-Jacobi quantization of O(3) nonlinear sigma model
• The Gauged O(3) Sigma Model: Schrödinger Representation and Hamilton-Jacobi Formulation

Cited by in corpus (4)

• Quantum deformation of the Dirac bracket
• Weyl's symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics
• Density resummation of perturbation series in a pion gas to leading order in chiral perturbation theory
• Underlying gauge symmetries of second-class constraints systems