2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56188For linear scalar field theories, I characterize those classical Hamiltonian vector fields which have self-adjoint operators as their quantum counterparts. As an application, it is shown that for a scalar field in curved space-time (in a Hadamard representation), a self-adjoint Hamiltonian for evolution along the unit timelike normal to a Cauchy surface exists only if the second fundamental form of the surface vanishes identically.30 pages, Latex2e with AMS packagesHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext