From general relativity to quantum gravity

Ashtekar, Abhay; Reuter, Martin; Rovelli, Carlo

doi:10.1007/3-540-11192-1_74

Cited by 22 publications

(45 citation statements)

References 161 publications

(367 reference statements)

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“…This general strategy is of course rather old (see, e.g., articles by Kuchař and Rovelli in [23] and the references they contain) although its full power does not seem to be always appreciated. What we wish to show in the next two subsections is: i) this strategy can be implemented in detail in all DIMT models; and, ii) the implementation enables us to ask and answer a number of "dynamical" questions of physical interest, including the fate of singularities.…”

Section: The Problemmentioning

confidence: 99%

“…Let us begin by noting that not all mathematically equivalent representations in quantum theory are suitable for addressing the issue of time. (For details, see, e.g., the article by Ashtekar in [23].) For the free relativistic particle, for example, time is explicit in the position representation; the quantum constraint equation, η ab ∇ a ∇ b Φ(x) = 0 can be immediately interpreted as the evolution equation.…”

Section: The Type I Modelmentioning

confidence: 99%

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Minisuperspaces: Observables and Quantization

Ashtekar

Tate

Uggla

1993

Int. J. Mod. Phys. D

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149

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A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit expressions of Dirac observables, i.e. phase space functions which commute weakly with the constraint. This, in turn, enables us to carry out a general quantization program to completion. We are also able to address the issue of time through "deparametrization" and discuss physical questions such as the fate of initial singularities in the quantum theory. We find that they persist in the quantum theory inspite of the fact that the evolution is implemented by a 1-parameter family of unitary transformations. Finally, certain of these models admit conditional symmetries which are explicit already prior to the canonical transformation. These can be used to pass to quantum theory following an independent avenue. The two quantum theories -based, respectively, on Dirac observables in the new canonical variables and conditional symmetries in the original ADM variables-are compared and shown to be equivalent.

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Section: The Problemmentioning

confidence: 99%

Section: The Type I Modelmentioning

confidence: 99%

Minisuperspaces: Observables and Quantization

Ashtekar

Tate

Uggla

1993

Int. J. Mod. Phys. D

Self Cite

149

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“…Now, if we have canonical transformation connecting (x, p) and (y, q), then using the realization given by eqns. (14) and (15) we can establish a canonical transformation between (ψ, φ) and (η, ζ). This in turn assures that the system described in terms of either (ψ, φ) or (η, ζ) refers to the same physical system.…”

Section: Stereographic Projection Using Non-commutative Coordinatesmentioning

confidence: 99%

“…But since we live in a quantum world, a complete understanding of gravity requires formulating a theory of gravity consistent with principles of quantum mechanics. In fact, quantum theory of gravity is a holy grail of theoretical physics and people have been attacking the problem of quantizing gravity along numerous paths but not yet have been succeeded [12,13,14,15]. The reasoning that spacetime loses the operational meaning as one goes to energy scale of order of Planck scale have lead to introduction of spacetime with non-commuting coordinates [16].…”

Section: Introductionmentioning

confidence: 99%

Regularization of Kepler problem in κ-spacetime

Guha

Harikumar

Zuhair

2016

Journal of Mathematical Physics

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In this paper we regularize the Kepler problem on κ-spacetime in several different ways. First, we perform a Moser-type regularization and then we proceed for the Ligon-Schaaf regularization to our problem. In particular, generalizing Heckman-de Laat (J. Symplectic Geom. 10, (2012), 463-473) in the noncommutative context we show that the Ligon-Schaaf regularization map following from an adaptation of the Moser regularization can be generalized to the Kepler problem on κ-spacetime.MSC primary 53D20, 37J15, 70H05, 70H33

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“…Essentially, these theories share the same problems of pure metric and Palatini theories of gravity [13,14,15]. In particular, the perturbative renormalizability or unitarity problems remain [16], as well as background independence [17,18] and so on.…”

Section: Introductionmentioning

confidence: 99%

Equivalence between the Lovelock–Cartan action and a constrained gauge theory

et al. 2017

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We show that the four-dimensional LovelockCartan action can be derived from a massless gauge theory for the SO(1, 3) group with an additional BRST trivial part. The model is originally composed of a topological sector and a BRST exact piece and has no explicit dependence on the metric, the vierbein or a mass parameter. The vierbein is introduced together with a mass parameter through some BRST trivial constraints. The effect of the constraints is to identify the vierbein with some of the additional fields, transforming the original action into the Lovelock-Cartan one. In this scenario, the mass parameter is identified with Newton's constant, while the gauge field is identified with the spin connection. The symmetries of the model are also explored. Moreover, the extension of the model to a quantum version is qualitatively discussed.

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From general relativity to quantum gravity

Cited by 22 publications

References 161 publications

Minisuperspaces: Observables and Quantization

Minisuperspaces: Observables and Quantization

Regularization of Kepler problem in κ-spacetime

Equivalence between the Lovelock–Cartan action and a constrained gauge theory

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