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The Stress-Energy Operator

Adam D. Helfer
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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.

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Adam D. Helfer. 1996-09-17. The Stress-Energy Operator. https://doi.org/10.1088/0264-9381%2F13%2F11%2F002

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