(2+1)-Dimensional Quantum Gravity

Hosoya, Akio; Nakao, Ken–ichi

doi:10.1143/ptp.84.739

Cited by 44 publications

(111 citation statements)

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“…Λ → 0 − Much of the classical behavior discussed above was studied previously in [1,5] for the case of vanishing cosmological constant. The Λ = 0 theory is easy to describe in ADM variables, but the holonomies analogous to R ± a are considerably more complicated, since the relevant gauge group is the non-semisimple Lie group ISO(2, 1), the (2+1)-dimensional Poincaré group.…”

Section: 2mentioning

confidence: 98%

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Comparative quantizations of (2+1)-dimensional gravity

Carlip

Nelson

1995

Phys. Rev. D

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We compare three approaches to the quantization of (2+1)-dimensional gravity with a negative cosmological constant: reduced phase space quantization with the York time slicing, quantization of the algebra of holonomies, and quantization of the space of classical solutions. The relationships among these quantum theories allow us to define and interpret time-dependent operators in the "frozen time" holonomy formulation. *

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Section: 2mentioning

confidence: 98%

“…This approach has been discussed in some detail by Moncrief [2] and Hosoya and Nakao [1]; in this section, we briefly summarize their results. We assume that spacetime has the topology IR ×Σ, where Σ is a closed genus g surface.…”

Section: Adm Formalismmentioning

confidence: 99%

Comparative quantizations of (2+1)-dimensional gravity

Carlip

Nelson

1995

Phys. Rev. D

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“…Quantization schemes for 2 + 1 dimensional gravity in absence of particles have been proposed in [8,9,10] and in presence of particles in [11,12,13].…”

Section: Introductionmentioning

confidence: 99%

ADM approach to 2+1 dimensional gravity

Menotti¹,

Seminara²

2000

Nuclear Physics B - Proceedings Supplements

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The canonical ADM equations are solved in terms of the conformal factor in the instantaneous York gauge. A simple derivation is given for the solution of the two body problem. A geometrical characterization is given for the apparent singularities occurring in the N -body problem and it is shown how the Garnier hamiltonian system arises in the ADM treatment by considering the time development of the conformal factor at the locations where the extrinsic curvature tensor vanishes. The equations of motion for the position of the particles and of the apparent singularities and also the time dependence of the linear residues at such singularities are given by the transformation induced by an energy momentum tensor of a conformal Liouville theory. Such an equation encodes completely the dynamics of the system.

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“…Three operatorsĴ ,M andĤ r should form a closed algebra in order to ensure the consistency among three wave equations (16), (19) and (24):…”

Section: Quantum Theorymentioning

confidence: 99%

Classical and quantum solutions of (2+1)-dimensional gravity under the de Broglie–Bohm interpretation

Kenmoku

Matsuyama

Sato

et al. 2002

Class. Quantum Grav.

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We have studied classical and quantum solutions of 2+1 dimensional Einstein gravity theory. Quantum theory is defined through the local conserved angular momentum and mass operators in the case of spherically symmetric space-time. The de Broglie-Bohm interpretation is applied for the wave function and we derive the differential equations for metrics. Metrics including quantum effect are obtained in solving these equations and we compare them with classical metrics. Especially the quantum effect on the closed de Sitter universe is evaluated quantitatively.

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(2+1)-Dimensional Quantum Gravity

Cited by 44 publications

References 0 publications

Comparative quantizations of (2+1)-dimensional gravity

Comparative quantizations of (2+1)-dimensional gravity

ADM approach to 2+1 dimensional gravity

Classical and quantum solutions of (2+1)-dimensional gravity under the de Broglie–Bohm interpretation

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