English

The Stress-Energy Operator

General Relativity and Quantum Cosmology 2010-04-06 v2

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.

Keywords

Cite

@article{arxiv.gr-qc/9602060,
  title  = {The Stress-Energy Operator},
  author = {Adam D. Helfer},
  journal= {arXiv preprint arXiv:gr-qc/9602060},
  year   = {2010}
}

Comments

Exposition improved. To appear in Letters to Classical and Quantum Gravity. Eight pp., plain Tex, IOP macros

R2 v1 2026-07-22T12:51:11.083Z