Topological matter coupled to gravity in 2 + 1 dimensions

Gegenberg, J.; Kunstatter, G.; Leivo, H.P.

doi:10.1016/0370-2693(90)90556-l

Cited by 8 publications

(12 citation statements)

References 9 publications

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“…Certain matter couplings in supergravity have been studied [104, 196], and work on circularly symmetric “midi-superspace models” has led to some surprising results, including unexpected bounds on the Hamiltonian [27, 32, 137, 53, 265, 224]. But the general problem of coupling matter remains very difficult, not least because — except in the special case of “topological matter” [140, 85] — we lose the ability to represent diffeomorphisms as ISO(2, 1) gauge transformations.Difficult as it is, however, an understanding of matter couplings may be the key to many of the conceptual issues of quantum gravity. One can explore the properties of a singularity, for example, by investigating the reaction of nearby matter, and one can look for quantization of time by examining the behavior of physical clocks.…”

Section: What Can We Still Learn?mentioning

confidence: 99%

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

Carlip

2005

Living Rev. Relativ.

108

120

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In three spacetime dimensions, general relativity drastically simplifies, becoming a “topological” theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2 + 1)-dimensional vacuum gravity in the setting of a spatially closed universe.

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Section: What Can We Still Learn?mentioning

confidence: 99%

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

Carlip

2005

Living Rev. Relativ.

108

120

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“…and as such it can be recognized as the Lie algebra of the inhomogeneized Poincaré group I(ISO(2, 1)) [5]. The Hamiltonian of the system is zero on shell, since it depends only on the constraints, and consequently the constraints are preserved in time.…”

Section: The Bcea Theorymentioning

confidence: 99%

Canonical analysis of the BCEA topological matter model coupled to gravitation in (2+1) dimensions

Freidel¹,

Mann²,

Popescu³

2005

Class. Quantum Grav.

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We consider a topological field theory derived from the Chern -Simons action in (2+1) dimensions with the I(ISO(2, 1)) group, and we investigate in detail the canonical structure of this theory.Originally developed as a topological theory of Einstein gravity minimally coupled to topological matter fields in (2+1) dimensions, it admits a BTZ black-hole solutions, and can be generalized to arbitrary dimensions. In this paper, we further study the canonical structure of the theory in (2+1) dimensions, by identifying all the distinct gauge equivalence classes of solutions as they result from holonomy considerations. The equivalence classes are discussed in detail, and examples of solutions representative of each class are constructed or identified. * Electronic address: lfreidel@perimeterinstitute.ca † Electronic address: mann@avatar.uwaterloo.ca ‡ Electronic address: empopesc@uwaterloo.ca

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“…Consider then a scalar field which will contribute 1/4 to K. To cancel this we need to couple it to a quantity that contributes −1/4 to K. This is achieved by coupling it to a rank two tensor field which contributes 3 × (3 − 4)/4.3 = −1/4. This is precisely the topological matter coupling considered in [4] with topological matter action given by:…”

Section: Path Integral Measure In Topological Field Theoriesmentioning

confidence: 99%