Living with ghosts
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- 9 May 2002
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 65 (10), 103515
- https://doi.org/10.1103/physrevd.65.103515
Abstract
Perturbation theory for gravity in dimensions greater than two requires higher derivatives in the free action. Higher derivatives seem to lead to ghosts, states with negative norm. We consider a fourth order scalar field theory and show that the problem with ghosts arises because, in the canonical treatment, and are regarded as two independent variables. Instead, we base quantum theory on a path integral, evaluated in Euclidean space and then Wick rotated to Lorentzian space. The path integral requires that quantum states be specified by the values of and To calculate probabilities for observations, one has to trace out over on the final surface. Hence one loses unitarity, but one can never produce a negative norm state or get a negative probability. It is shown that transition probabilities tend toward those of the second order theory, as the coefficient of the fourth order term in the action tends to zero. Hence unitarity is restored at the low energies that now occur in the universe.
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This publication has 11 references indexed in Scilit:
- Trace anomaly driven inflationPhysical Review D, 2001
- Does back reaction enforce the averaged null energy condition in semiclassical gravity?Physical Review D, 1996
- Einstein equation with quantum corrections reduced to second orderPhysical Review D, 1993
- No Starobinsky inflation from self-consistent semiclassical gravityPhysical Review D, 1992
- Renormalizable asymptotically free quantum theory of gravityNuclear Physics B, 1982
- A new type of isotropic cosmological models without singularityPhysics Letters B, 1980
- 1N expansion and renormalization in quantum gravityPhysics Letters B, 1977
- Renormalization of higher-derivative quantum gravityPhysical Review D, 1977
- Matrix for Gravitational Field. II. Local Measure; General Relations; Elements of Renormalization TheoryPhysical Review D, 1973
- Renormalization of a Classical Gravitational Field Interacting with Quantized Matter FieldsJournal of Mathematical Physics, 1962