On Quantization of Polynomial Momentum Observables

TL;DR

This paper introduces a new quantization method for polynomial momentum observables on manifolds, enabling broader quantization of functions, and applies it to quantum mechanics of particles in curved space-time.

Contribution

A novel quantization procedure for polynomial momentum observables is developed and applied to quantum mechanics in curved space-time.

Findings

Quantization method applicable to polynomials of any order in momenta.

Successful application to scalar particles in curved space-time.

Broadens the scope of quantization techniques for geometric observables.

Abstract

The paper is devoted to quantization of polynomial momentum observables in the cotangent bundle of a smooth manifold. A quantization procedure is proposed allowing to quantize a wide class of functions which are polynomials of any order in momenta. In the last part of the paper the quantum mechanics of scalar particle in curved space-time is studied with the use of proposed approach.