Towards canonical quantum gravity forG1geometries in 2+1 dimensions with a Λ-term

DOI10.1088/0264-9381/25/23/235014zbMATH Open1155.83335arXiv0806.0137OpenAlexW3106338962MaRDI QIDQ5302161

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Publication date: 6 January 2009

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Abstract: The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper imposition of the quantum analogues of the two linear (momentum) constraints reduces an initial collection of state vectors, consisting of all smooth functionals of the components (and/or their derivatives) of the spatial metric, to particular scalar smooth functionals. The demand that the midi-superspace metric (inferred from the kinetic part of the quadratic (Hamiltonian) constraint) must define on the space of these states an induced metric whose components are given in terms of the same states, which is made possible through an appropriate re-normalization assumption, severely reduces the possible state vectors to three unique (up to general coordinate transformations) smooth scalar functionals. The quantum analogue of the Hamiltonian constraint produces a Wheeler-DeWitt equation based on this reduced manifold of states, which is completely integrated.

Full work available at URL: https://arxiv.org/abs/0806.0137

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