C. Destri et al., ON THE DEFINITION OF QUANTUM FREE PARTICLE ON CURVED MANIFOLDS, Nuovo cimento della Società Italiana di Fisica. A. Nuclei, particles and fields, 107(2), 1994, pp. 237-241
A self-consistent definition of quantum free particle on a generic cur
ved manifold naturally emerges by restricting the dynamics to submanif
olds of co-dimension one.