Gauge invariant counterparts and quantization of systems under holonomic constraints

TL;DR

This paper reveals hidden gauge symmetries in systems with holonomic constraints, enabling their quantization as first-class systems directly in phase space, demonstrated through particle and field theory examples.

Contribution

It introduces a method to identify gauge invariances in constrained systems and quantize them without converting to second-class form, applicable to particles and field theories.

Findings

Hidden gauge symmetry exists in holonomic constrained systems.

Quantization as first-class systems is feasible in original phase space.

Applications include particle motion on spheres and nonlinear sigma models.

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.