Algebraic Constraint Quantization and the Pseudo-Rigid Body

TL;DR

This paper applies an algebraic constraint quantization scheme to a pseudo-rigid body system with a nonunimodular gauge group, resulting in a unique quantum description of its physical degrees of freedom.

Contribution

It demonstrates that the nonunimodular gauge group constraint does not restrict the observable content, leading to a unique quantization aligned with the CM(N) model.

Findings

The nonunimodular gauge constraint does not restrict observables.

The quantization yields a realization of the CM(N) collective motion model.

The scheme provides a consistent quantum description of the constrained system.

Abstract

The pseudo--rigid body represents an example of a constrained system with a nonunimodular gauge group. This system is treated along the guidelines of an algebraic constraint quantization scheme which focusses on observable quantities, translating the vanishing of the constraints into representation conditions on the algebra of observables. The constraint which is responsible for the nonunimodularity of the gauge group is shown not to contribute to the observable content of the constraints, i.e., not to impose any restrictions on the construction of the quantum theory of the system. The application of the algebraic constraint quantization scheme yields a unique quantization of the physical degrees of freedom, which are shown to form a realization of the so-called CM(N) model of collective motions.