General Relativity and Gravitation

, Volume 17, Issue 6, pp 573–578 | Cite as

A constraint on physical quantum states in cosmological space-times

  • A. H. Najmi
  • A. C. Ottewill
Research Articles


The problem of constructing the Hilbert space of physical states for a free scalar quantum field propagating on a cosmological background is considered. The concept of energy-momentum for such a field is discussed and it is noted that, according to current renormalization theory, for a state ¦M〉 to have finite energy density its associated anticommutator function\(\left\langle {M\left| {\widehat\phi \left( x \right)\widehat\phi \left( {x'} \right) + \widehat\phi \left( {x'} \right)\widehat\phi \left( x \right)} \right|M} \right\rangle \) must be of a particular form first discussed by Hadamard. This restriction is shown to lead to a constraint on the construction of the Hilbert space of physical states. This constraint is used to reject a recently proposed scheme for the construction of this space which was based on a principle of energy minimization.


Physical State Energy Density Hilbert Space Quantum State Energy Minimization 


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Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • A. H. Najmi
    • 1
  • A. C. Ottewill
    • 2
  1. 1.Department of PhysicsUniversity of UtahSalt Lake City
  2. 2.Enrico Fermi InstituteUniversity of ChicagoChicago

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