Probability Interpretation for Klein-Gordon Fields and the Hilbert Space Problem in Quantum Cosmology

Details Probability Interpretation for Klein-Gordon Fields and the Hilbert Space Problem in Quantum Cosmology Probability Interpretation for Klein-Gordon Fields and the Hilbert Space Problem in Quantum Cosmology

2002-05-13

arxiv.org/abs/gr-qc/0205049v4

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, references added, slightly revised version

Scientific paper

We give an explicit construction of a positive-definite invariant inner-product for the Klein-Gordon fields, thus solving the old problem of the probability interpretation of Klein-Gordon fields without having to restrict to the subspaces of the positive-frequency solutions. Our method has a much wider domain of application and may be used to obtain the most general invariant inner-product on the solution space of a broad class of Klein-Gordon type evolution equations. We explore its consequences for the solutions of the Wheeler-DeWitt equation associated with the FRW-massive-real-scalar-field models.

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