The Hamiltonians of Linear Quantum Fields: I. Existence Theory
arXiv:hep-th/9908011
Abstract
For 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.
arXiv comment30 pages, Latex2e with AMS packages
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