The stress-energy operator

We compute the stress-energy operator for a scalar linear quantum held in curved spacetime, modulo c-numbers. For the associated Hamiltonian operators, even those generating evolution along timelike vector fields, we find that, in general, on locally Fock-like ('Hadamard') representations: (a) the Hamiltonians cannot be self-adjoint operators; (b) the automorphisms of the field algebra generated by the evolution cannot be unitarily implemented; (c) the expectation values of the Hamiltonians are well defined on a dense family of states; but (d) these expectation values am unbounded below, even for evolution along future-directed timelike vector fields and even on Hadamard states. These are all local, ultraviolet, effects.