A note on quantization of a free particle in the Zoll manifold

Abstract

This note studies the spectrum of the quantum Hamiltonian operator corresponding to the classical Hamiltonian of a free particle in the Zoll manifold, and clarifies the effect of the zero-th order term defined from the curvature of the configuration space. It is shown that the zero-th order term R/6 (R; scalar curvature) has a special meaning in view of the energy spectrum.