### Abstract

Hamiltonian structures for spatially compact locally homogeneous vacuum universes are investigated, provided that the set of dynamical variables contains the Teichmüller parameters, parameterizing the purely global geometry. One of the key ingredients of our arguments is a suitable mathematical expression for quotient manifolds, where the universal cover metric carries all the degrees of freedom of geometrical variations, i.e., the covering group is fixed. We discuss general problems concerned with the use of this expression in the context of general relativity, and demonstrate the reduction of the Hamiltonians for some examples. For our models, all the dynamical degrees of freedom in Hamiltonian view are unambiguously interpretable as geometrical deformations, in contrast to the conventional open models.

Original language | English |
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Pages (from-to) | 6560-6577 |

Number of pages | 18 |

Journal | Journal of Mathematical Physics |

Volume | 38 |

Issue number | 12 |

Publication status | Published - 1997 Dec |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Journal of Mathematical Physics*,

*38*(12), 6560-6577.

**Hamiltonian structures for compact homogeneous universes.** / Tanimoto, Masayuki; Koike, Tatsuhiko; Hosoya, Akio.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 38, no. 12, pp. 6560-6577.

}

TY - JOUR

T1 - Hamiltonian structures for compact homogeneous universes

AU - Tanimoto, Masayuki

AU - Koike, Tatsuhiko

AU - Hosoya, Akio

PY - 1997/12

Y1 - 1997/12

N2 - Hamiltonian structures for spatially compact locally homogeneous vacuum universes are investigated, provided that the set of dynamical variables contains the Teichmüller parameters, parameterizing the purely global geometry. One of the key ingredients of our arguments is a suitable mathematical expression for quotient manifolds, where the universal cover metric carries all the degrees of freedom of geometrical variations, i.e., the covering group is fixed. We discuss general problems concerned with the use of this expression in the context of general relativity, and demonstrate the reduction of the Hamiltonians for some examples. For our models, all the dynamical degrees of freedom in Hamiltonian view are unambiguously interpretable as geometrical deformations, in contrast to the conventional open models.

AB - Hamiltonian structures for spatially compact locally homogeneous vacuum universes are investigated, provided that the set of dynamical variables contains the Teichmüller parameters, parameterizing the purely global geometry. One of the key ingredients of our arguments is a suitable mathematical expression for quotient manifolds, where the universal cover metric carries all the degrees of freedom of geometrical variations, i.e., the covering group is fixed. We discuss general problems concerned with the use of this expression in the context of general relativity, and demonstrate the reduction of the Hamiltonians for some examples. For our models, all the dynamical degrees of freedom in Hamiltonian view are unambiguously interpretable as geometrical deformations, in contrast to the conventional open models.

UR - http://www.scopus.com/inward/record.url?scp=0031527118&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031527118&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031527118

VL - 38

SP - 6560

EP - 6577

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 12

ER -