Canonical Structure of Locally Homogeneous Systems on Compact Closed 3-Manifolds of Types E^3, Nil and Sol

概要

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In this paper we investigate the canonical structure of diffeomorphism-invariant phase spaces for spatially locally homogeneous spacetimes with 3-dimensional compact closed spaces. After giving a general algorithm to express the diffeomorphism-invariant phase space and the canonical structure of a locally homogeneous system in terms of those of a homogeneous system on a covering space and a moduli space, we determine completely the symplectic structures and the Hamiltonians of locally homogeneous pure gravity systems on orientable, compact closed 3-spaces of the Thurston-type E^3, Nil and Sol for all possible space topologies and invariance groups. We point out that in many cases the symplectic structure of the phase space becomes degenerate in the moduli sector. This implies that locally homogeneous systems are not canonically closed in general in the full diffeomorphism-invariant phase space of generic spacetimes with compact closed spaces.
理論物理学刊行会の論文
1998-02-25