A Higuchi 1991 Class. Quantum Grav. 8 2023 doi:10.1088/0264-9381/8/11/012
A Higuchi
Show affiliationsIt is known that quadratic constraints must be imposed on linearized gravity in a spacetime with compact Cauchy surfaces and with Killing vectors. These constraints cannot be derived from the linearized Lagrangian. They require that the quantum states be invariant under the continuous isometry group of the background spacetime. This fact makes it non-trivial to construct a Hilbert space of linearized gravity in some spacetimes with compact Cauchy surfaces. A method for dealing with this problem has been proposed for the case of de Sitter spacetime. It is shown that this method can be used to construct a Hilbert space of linearized gravity in flat space with toroidal topology. The inner product is shown to be a modified Klein-Gordon inner product. Some speculations are made about applying this method to full quantum gravity.
04.20.Cv Fundamental problems and general formalism
04.20.Gz Spacetime topology, causal structure, spinor structure
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
Issue 11 (November 1991)
A Higuchi 1991 Class. Quantum Grav. 8 2023
K Shiraishi 1990 Class. Quantum Grav. 7 135
K Shiraishi 1989 Class. Quantum Grav. 6 2029
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