Monopole Gauge Fields and Quantum Potentials Induced by the Geometry in Simple Dynamical Systems

TL;DR

This paper demonstrates how geometric constraints in quantum systems induce gauge fields and quantum potentials, affecting molecular rotational dynamics and revealing monopole-like structures in effective Hamiltonians.

Contribution

It provides explicit examples showing the emergence of abelian and non-abelian gauge fields from geometrical constraints in simple quantum systems.

Findings

Effective Hamiltonians mimic charged particles in magnetic-monopole fields.

Explicit non-abelian monopole-like fields are derived for spherical top molecules.

Quantum potentials influence rotovibrational interactions in molecules.

Abstract

A realistic analysis shows that constraining a quantomechanical system produces the effective dynamics to be coupled with {\sl abelian/non-abelian gauge fields} and {\sl quantum potentials} induced by the {\sl intrinsic} and {\sl extrinsic geometrical properties} of the constraint's surface. This phenomenon is observable in the effective rotational motion of some simple polyatomic molecules. By considering specific examples it is shown that the effective Hamiltonians for the nuclear rotation of linear and symmetric top molecules are equivalent to that of a charged system moving in a background magnetic-monopole field. For spherical top molecules an explicit analytical expression of a non-abelian monopole-like field is found. Quantum potentials are also relevant for the description of rotovibrational interactions.