Algebraic analysis of a model of two-dimensional gravity

Frolov, Alexei M.; Kiriushcheva, N.; Kuzmin, S. V.

doi:10.1007/s10714-010-0935-2

Cited by 2 publications

(2 citation statements)

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“…Hence, the breakdown in space-time is a non-perturbative property of GR (for d ≥ 2) itself. In the following section, we present a summary of results derived in [9][10][11][12][13], whereby, based on these findings we propose that the loss of manifest covariance using the constraint quantization approach is due to its application on the full action. To support our claims, we present a counterexample regarding the successful quantization of non-Abelian gauge Yang Mills theories, where covariance is recovered in the path integral [13].…”

Section: Introductionmentioning

confidence: 94%

“…where B αβγµνρ = g αβ g γρ g µν − g αµ g βν g γρ + 2g αρ g βν g γµ − 2g αβ g γµ g νρ . For this action, it was found that the constraints are first class [11] for d > 2 dimensions, and similarly for d = 2 dimensions [12] for which the following path integral by Fadeev [17] applies:…”

Section: Canonical Quantization Of D ≥ 2 Dimensional Gr Via Canonical...mentioning

confidence: 99%

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On the breakdown of space-time in General Relativity

Chishtie¹

2021

Preprint

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Based on the canonical quantization of d ≥ 2 dimensional General Relativity (GR) via the Dirac constraint formalism (also termed as 'constraint quantization'), we propose the loss of covariance as a fundamental property of the theory. This breakdown occurs for the first-order Einstein Hilbert action, whereby besides first class constraints, second class constriants also exist leading to non-standard ghost fields which render the path integral non-covariant. For the Hamiltonian formulation of GR, only first class constraints exist, however, the loss of covariance still happens due to structures arising from non-covariant constraints in the path integral. In contrast, covariance is preserved when constraint quantization is conducted for non-Abelian gauge theories, such as the Yang-Mills theory. Hence, we infer that the breakdown in space-time is a property of GR itself (for d ≥ 2 dimensions). Covariance is recovered and quantization and perturbative calculations are possible in the weak limit of the gravitational field of these actions. Hence, we further propose that the breakdown of space-time occurs as a non-perturbative feature of GR in the strong limit of the theory. These findings are novel from a canonical gravity formalism standpoint, and are consistent with GR singularity theorems which indicate breakdown at a strong limit of the field. They also support emergent theories of spacetime and gravity, though do not require thermodynamics such as entropic gravity. From an effective field theory view, these indicate that new degrees of freedom in the nonperturbative sector of the full theory are a requirement, whereby covariance as a symmetry is broken in the high energy (strong field) sector. Our findings are also consistent with the recent resolution of the information loss paradox in black holes.

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Section: Introductionmentioning

confidence: 94%

Section: Canonical Quantization Of D ≥ 2 Dimensional Gr Via Canonical...mentioning

confidence: 99%

On the breakdown of space-time in General Relativity

Chishtie¹

2021

Preprint

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On the breakdown of space–time in general relativity

Chishtie

2023

Can. J. Phys.

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Based on the canonical quantization of $d>2$ dimensional General Relativity (GR) via the Dirac constraint formalism (also termed as `constraint quantization'), we propose the loss of covariance as a fundamental property of the theory. This breakdown occurs for the first-order Einstein Hilbert action, whereby loss of diffeomorphism invariance, besides first class constraints, second class constriants also exist leading to non-standard ghost fields which render the path integral non-covariant. We also attempt, for the first time, the canonical quantization via calculation of the path integral for the equivalent Hamiltonian formulation of GR for which only first class constraints exist. However, loss of covariance still occurs in this action due to loss of diffeomorphism invariance and structures arising from non-covariant constraints in the path integral. In contrast, we find that covariance as a symmetry is restored and quantization with perturbative calculations is possible in the weak limit of the gravitational field of these actions. Hence, we firstly establish, for the first time, that the breakdown in space-time is a property of GR itself as its limitation, indicating it to be an Effective Field Theory (EFT). We further propose that the breakdown of space-time occurs as a non-perturbative feature of GR in the strong field limit of the theory. Besides GR, we also note that covariance is preserved when constraint quantization is conducted for non-Abelian gauge theories, such as the Yang-Mills theory. These findings are novel from a canonical gravity formalism and EFT approach, and are consistent with GR singularity theorems, yet are general and extend them, as the singularity theorems indicate breakdown at a strong field limit of GR in black holes. Our findings are in contrast to the asymptotic safety program. They support emergent theories of space-time and gravity, though are unique, as they do not require thermodynamics.

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Algebraic analysis of a model of two-dimensional gravity

Cited by 2 publications

References 29 publications

On the breakdown of space-time in General Relativity

On the breakdown of space-time in General Relativity

On the breakdown of space–time in general relativity

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