Journal ArticleDOI
Exact quantum scattering in 2 + 1 dimensional gravity
TLDR
In this article, exact multiparticle scattering amplitudes are computed in terms of expectation values of Wilson lines, and the two-particle amplitude reduces to an earlier result of 't Hooft.About:
This article is published in Nuclear Physics.The article was published on 1989-09-18. It has received 155 citations till now. The article focuses on the topics: Quantum gravity & Hořava–Lifshitz gravity.read more
Citations
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Topological field theory
Journal ArticleDOI
What Is Observable in Classical and Quantum Gravity
TL;DR: In this paper, the problem of identifying the observable quantities in quantum gravity (or in any diffeomorphism invariant quantum theory) is considered, and it is shown that only by explicitly taking into account the physical nature of the bodies that form the reference system and their gravitational interactions one can get well defined gauge-invariant (and local) observables and a definition of physical spacetime points.
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Quantization of point particles in (2+1)-dimensional gravity and spacetime discreteness
TL;DR: In this paper, the authors investigated the canonical commutation rules for gravitating quantized particles in a (2 + 1)-dimensional world and found that these particles live on a spacetime lattice.
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Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
TL;DR: In this paper, the authors studied three-dimensional Chern-Simons theory with complex gauge group SL(2,ℂ) and showed that the classical and quantum properties of such theory are described by an algebraic curve called the A-polynomial of a knot.
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Quantization of Chern-Simons gauge theory with complex gauge group
TL;DR: The canonical quantization of Chern-Simons gauge theory in 2+1 dimensions is generalized from the case in which the gauge group is a compact Lie group to the case of a complex Lie group as mentioned in this paper.
References
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Journal ArticleDOI
Quantum field theory and the Jones polynomial
TL;DR: In this paper, it was shown that 2+1 dimensional quantum Yang-Mills theory with an action consisting purely of the Chern-Simons term is exactly soluble and gave a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.
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(2+1)-Dimensional Gravity as an Exactly Soluble System
TL;DR: By disentangling the hamiltonian constraint equations, 2 + 1 dimensional gravity (with or without a cosmological constant) is shown to be exactly soluble at the classical and quantum levels.
Book
Braids, Links, and Mapping Class Groups
TL;DR: Artin's braid group has been studied extensively in the literature as discussed by the authors, where structural and algebraic properties of the braid groups of two manifolds of two different scales have been studied.
Journal ArticleDOI
Role of surface integrals in the Hamiltonian formulation of general relativity
T. Regge,Claudio Teitelboim +1 more
TL;DR: In this article, it is shown that if the phase space of general relativity is defined so as to contain the trajectories representing solutions of the equations of motion then, for asymptotically flat spaces, the Hamiltonian does not vanish but its value is given rather by a nonzero surface integral.
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Quantum Mechanics of Fractional-Spin Particles
TL;DR: In this article, the statistics of two-particle quantum mechanics are discussed, and how this works for two-and three-dimensional quantum mechanics is discussed in the context of (2+1)-and (3+3)-models.