The Stress-Energy Operator
arXiv:gr-qc/9602060 · doi:10.1088/0264-9381/13/11/002
Abstract
We compute the stress--energy operator for a scalar linear quantum field in curved space-time, 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 are unbounded below, even for evolution along future-directed timelike vector fields and even on Hadamard states. These are all local, ultraviolet, effects.
Exposition improved. To appear in Letters to Classical and Quantum Gravity. Eight pp., plain Tex, IOP macros
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