Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe

Carlip, Steven

doi:10.12942/lrr-2005-1

Cited by 108 publications

(126 citation statements)

References 263 publications

(519 reference statements)

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“…[18], [19], and [20], there is no complete Hamiltonian formulation of tetrad gravity in three dimensions. The only papers that somehow related to tetrad gravity in three dimensions are: the work due to Blagojević and Cvetković [21] where all steps of the Dirac procedure were performed, but for the three dimensional Mielke-Baekler model;…”

Section: Introductionmentioning

confidence: 99%

The Hamiltonian formulation of tetrad gravity: Three-dimensional case

2010

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The Hamiltonian formulation of the tetrad gravity in any dimension higher than two, using its first order form when tetrads and spin connections are treated as independent variables, is discussed and the complete solution of the three dimensional case is given. For the first time, applying the methods of constrained dynamics, the Hamiltonian and constraints are explicitly derived and the algebra of the Poisson brackets among all constraints is calculated. The algebra of the Poisson brackets among first class secondary constraints locally coincides with Lie algebra of the ISO(2,1) Poincaré group. All the first class constraints of this formulation, according to the Dirac conjecture and using the Castellani procedure, allow us to unambiguously derive the generator of gauge transformations and find the gauge transformations of the tetrads and spin connections which turn out to be the same found by Witten without recourse to the Hamiltonian methods [Nucl. Phys. B 311 (1988) 46 ]. The gauge symmetry of the tetrad gravity generated by Lie algebra of constraints is compared with another invariance, diffeomorphism. Some conclusions about the Hamiltonian formulation in higher dimensions are briefly discussed; in particular, that diffeomorphism invariance is not derivable as a gauge symmetry from the Hamiltonian formulation of tetrad gravity in any dimension when tetrads and spin connections are used as independent variables.

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Section: Introductionmentioning

confidence: 99%

The Hamiltonian formulation of tetrad gravity: Three-dimensional case

2010

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“…In three spacetime dimensions, general relativity is a "topological" theory, with only a finite, and typically small, number of global degrees of freedom [2]. The BTZ black hole, on the other hand, can have an arbitrarily large entropy.…”

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confidence: 99%

“…and determine (2) f and (2) h i by demanding that the metric remain in the form (1). It is easy to check that…”

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confidence: 99%

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Dynamics of asymptotic diffeomorphisms in (2+1)-dimensional gravity

Carlip

2005

Class. Quantum Grav.

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“…The physics of (2+1)-space has attracted considerable attention in different branches of physics, such as the theory of graphene [1], black holes [2,3], quantum gravity [4], the AdS/CFT correspondence [5], and the gauge theory of gravity [6,7]. It is well known that rotations of 3D Euclidean and Minkowski spaces can be represented by the algebra of Hamilton's and split quaternions, respectively.…”

Section: Introductionmentioning

confidence: 99%

Split quaternions and particles in (2+1)-space

Gogberashvili

2014

Eur. Phys. J. C

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It is well known that quaternions represent rotations in 3D Euclidean and Minkowski spaces. However, the product by a quaternion gives rotation in two independent planes at once and to obtain single-plane rotations one has to apply half-angle quaternions twice from the left and on the right (with inverse). This 'double-cover' property is a potential problem in the geometrical application of split quaternions, since the (2+2)-signature of their norms should not be changed for each product. If split quaternions form a proper algebraic structure for microphysics, the representation of boosts in (2+1)-space leads to the interpretation of the scalar part of quaternions as the wavelengths of particles. The invariance of space-time intervals and some quantum behaviors, like noncommutativity and the fundamental spinor representation, probably also are algebraic properties. In our approach the Dirac equation represents the CauchyRiemann analyticity condition and two fundamental physical parameters (the speed of light and Planck's constant) emerge from the requirement of positive definiteness of the quaternionic norms.

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Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe

Cited by 108 publications

References 263 publications

The Hamiltonian formulation of tetrad gravity: Three-dimensional case

The Hamiltonian formulation of tetrad gravity: Three-dimensional case

Dynamics of asymptotic diffeomorphisms in (2+1)-dimensional gravity

Split quaternions and particles in (2+1)-space

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