Canonical Quantum Gravity

Cianfrani, Francesco; Lecian, Orchidea Maria; Lulli, Matteo; Montani, Giovanni

doi:10.1142/8957

Cited by 49 publications

(69 citation statements)

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“…Focusing on the probabilistic interpretation for the wave function, De Witt [1] first suggested to define a scalar product from a conserved current j µ , analogously to the Klein-Gordon case. Although a Klein-Gordon-like current can be defined, the corresponding scalar product is not positive defined and no separation of frequencies can be consistently implemented (this is due to a divergence occurring in superspace when the metric determinant vanishes, see for instance [6]). …”

Section: Semiclassical Approximationmentioning

confidence: 99%

“…The minisuperspace model [5,6] is a natural arena for the study of Quantum Cosmology, since, as soon as we consider homogeneous Universes (Bianchi models) [7], the corresponding wave function is taken over a finite number of degrees of freedom, typically the three cosmic scale factors (or some functions of them), determining the evolution of independent spatial directions.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic interpretation of the wave function for the Bianchi I model

2017

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We compare two different approaches for quantization of the Bianchi I model: a reduced phase space quantization, in which the isotropic Misner variables is taken as time, and the Vilenkin proposal, in which a semiclassical approximation is performed for the same variable. We outline the technical and interpretative issues of these two methods and we demonstrate that they provide equivalent results only if the dynamics is essentially dictated by the isotropic matter contribution.

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Section: Semiclassical Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Probabilistic interpretation of the wave function for the Bianchi I model

2017

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“…6.4 in Ref. 1. From the Holst action it is plausible that the parameter is related to torsion and parity violation since β is an effective coupling constant of the parity-odd Ricci scalar.…”

Section: Introductionmentioning

confidence: 99%

Implementation of conformal scaling in loop quantum gravity via the Barbero-Immirzi parameter

Wong¹

2017

The Fourteenth Marcel Grossmann Meeting

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The Barbero-Immirzi parameter of loop quantum gravity is a one parameter ambiguity of the theory whose physical significance is as-of-yet unknown. It is an inherent characteristic of the quantum theory since it appears in the spectra of geometric operators. The parameter's appearance in the area and volume spectra imply that it plays a role in determining the fundamental length scale of space. This appearance as a rescaling of lengths motivates a possible conformal interpretation. Presented here is an analysis of the conformal scaling of the triad formalism and the revelation that the Barbero-Immirzi parameter precisely corresponds to the conformal scale factor. Furthermore, at the kinematical level the conformal scale factor materializes as a scalar field coupled to gravity. The development of this conformal scalar field to the quantum sector of the theory is also sketched.

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“…This truism was explicitly confirmed in [4,9] by the calculation of Poisson brackets (PBs) among the phase-space variables. Waxing poetic, the term "the non-canonicity puzzle" was coined in [10] to describe the results of [4,9]; but in [11], using more direct language, it is called "the contradiction that again witnesses about the incompleteness of the theoretical foundations". The source of the "puzzle" or "contradiction" lies in finding how to reconcile the non-equivalence of the two Hamiltonian formulations with their corresponding Lagrangian formulations when "it is supposed" [12] or "it is believed" (as in [11]) "that each of them is equivalent to the Einstein (Lagrangian) formulation" [11,12].…”

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confidence: 99%

“…This belief might lead one to conclude that Dirac's Hamiltonian formulation of constrained systems is incomplete [11], and proposals ought to follow on how to redefine the primary constraints, on how to use boundary terms, on how to have "two non-canonical transformations that compensate each other" [10], and on how to modify the PBs through the extension of phase space 2 [11,12]. But such approaches immediately give rise to a general question: why are such manipulations needed for one formulation (i.e.…”

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confidence: 99%

Remarks on the “Non-canonicity Puzzle”: Lagrangian Symmetries of the Einstein-Hilbert Action

2012

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Given the non-canonical relationship between variables used in the Hamiltonian formulations of the Einstein-Hilbert action (due to Pirani, Schild, Skinner (PSS) and Dirac) and the Arnowitt-Deser-Misner (ADM) action, and the consequent difference in the gauge transformations generated by the first-class constraints of these two formulations, the assumption that the Lagrangians from which they were derived are equivalent leads to an apparent contradiction that has been called "the non-canonicity puzzle". In this work we shall investigate the group properties of two symmetries derived for the Einstein-Hilbert action: diffeomorphism, which follows from the PSS and Dirac formulations, and the one that arises from the ADM formulation. We demonstrate that unlike the diffeomorphism transformations, the ADM transformations (as well as others, which can be constructed for the Einstein-Hilbert Lagrangian using Noether's identities) do not form a group. This makes diffeomorphism transformations unique (the term "canonical" symmetry might be suggested). If the two Lagrangians are to be called equivalent, canonical symmetry must be preserved. The interplay between general covariance and the canonicity of the variables used is discussed.

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Canonical Quantum Gravity

Cited by 49 publications

References 0 publications

Probabilistic interpretation of the wave function for the Bianchi I model

Probabilistic interpretation of the wave function for the Bianchi I model

Implementation of conformal scaling in loop quantum gravity via the Barbero-Immirzi parameter

Remarks on the “Non-canonicity Puzzle”: Lagrangian Symmetries of the Einstein-Hilbert Action

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