MONOPOLE GAUGE-FIELDS AND QUANTUM POTENTIALS INDUCED BY THE GEOMETRY IN SIMPLE DYNAMICAL-SYSTEMS

A realistic analysis shows that constraining a quantum mechanical syst em produces the effective dynamics to be coupled with Abelian/non-Abel ian gauge fields and quantum potentials induced by the intrinsic and e xtrinsic geometrical properties of the constraint's surface. This phen omenon is observable in the effective rotational motion of some simple polyatomic molecules. By considering specific examples it is shown th at the effective Hamiltonians for the nuclear rotation of linear and s ymmetric top molecules are equivalent to that of a charged system movi ng in a background magnetic-monopole field. For spherical top molecule s an explicit analytical expression of a non-Abelian monopole-like fie ld is found. Quantum potentials are also relevant for the description of rotovibrational interactions. (C) 1996 Academic Press, Inc.