English

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

General Relativity and Quantum Cosmology 2007-05-23 v4 High Energy Physics - Theory Mathematical Physics math.MP Quantum Physics

Abstract

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.

Keywords

Cite

@article{arxiv.gr-qc/0205049,
  title  = {Probability Interpretation for Klein-Gordon Fields and the Hilbert Space Problem in Quantum Cosmology},
  author = {Ali Mostafazadeh},
  journal= {arXiv preprint arXiv:gr-qc/0205049},
  year   = {2007}
}

Comments

11 pages, references added, slightly revised version

R2 v1 2026-07-22T12:35:42.231Z