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Cited by 529Noncommutative and Quantum Gravity TheoriesCosmology and Gravitation TheoriesRelativity and Gravitational Theory

Quantum Cosmology. I

Misner, Charles W.·1969·Physical Review
DOI 10.1103/physrev.186.1319
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Abstract

The Hamiltonian methods of Arnowitt, Deser, and Misner can be applied to homogeneous cosmological models, and prove to be an efficient way both of constructing the Einstein equations and of studying their solutions. By using an appropriate form for the metric, one finds that the constraint equations for these models can be solved explicitly, and the resulting problem in Hamiltonian mechanics resembles that of a particle in a potential well. The most unusual feature of the Hamiltonian is that it is explicitly time dependent. There is an easy and attractive choice of factor orderings which allows one to pass on to a quantum theory (by imposing canonical commutation relations on the independent canonical variables) while maintaining the signature of the quantized metric. For the closed-space cosmological model (Bianchi type IX) which is studied in most detail, a classical (high-quantum-number) state remains classical as the wave function is followed back in time toward the initial singularity. There is no tendency for significant contributions from states of low quantum number to develop even when the radius of the universe is much less than ${(\frac{G\ensuremath{\hbar}}{{c}^{3}})}^{\frac{1}{2}}={10}^{\ensuremath{-}33}$ cm.

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  • Homogeneous minisuperspace models reduce the infinite number of degrees of freedom of general relativity to finitely many.

    “This symmetry condition reduces the infinite number of degrees of freedom of general relativity to finitely many ones for these homogeneous minisuperspace models [1,2]”

    From Loop quantum cosmology: I. Kinematics (2000) · cites this paper as [2]

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Authors
Misner, C. W.
Affiliations
University of Maryland, College Park (US)
Corresponding author
Misner, Charles W.
ORCID
Misner, Charles W.
Venue
Physical Review
Publisher
American Physical Society (APS)
Published
1969-10-25
Volume
186
Issue
5
Pages
1319-1327
ISSN
0031-899X (ISSN-L)
DOI
10.1103/physrev.186.1319
OpenAlex
W2043260986
Cited by
529
References
29
Citations by year
2026: 12 · 2025: 16 · 2024: 11 · 2023: 10 · 2022: 10 · 2021: 11 · 2020: 29 · 2019: 11 · 2018: 8 · 2017: 22 · 2016: 18 · 2015: 10 · 2014: 12 · 2013: 16 · 2012: 11
FWCI
30.88
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
Physical Review (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
Keywords
quantum cosmology, ADM formalism, homogeneous cosmological models, Bianchi type IX, closed universe, initial singularity, constraint equations, time-dependent Hamiltonian, factor ordering, canonical commutation relations, quantum states, classical limit

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