Construction of position and momentum operators and hamiltonians by embedding and submersion

Extrinsic position and momentum operators are defined on a manifold M via an embedding i:M → (Rsub(n), gsub(n)) and, via a submersion, π:Rsub(n) → M. A Hamiltonian H0, describing free dynamics on M, is constructed as an intrinsic property of M by the embedding i and an associated Riemannian geodesic submersion. (orig.)