Manifestly Covariant Canonical Formalism of Quantum Gravity - Systematic Presentation of the Theory

Nakanishi, Noboru

doi:10.2977/prims/1195182022

Cited by 17 publications

(5 citation statements)

References 46 publications

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“…Transition amplitudes of the form L + |L − constitute the S-matrix. In agreement with this section's reasoning, no holographic behavior is known in this relatively well-studied system of observables [20,21].…”

Section: The S-matrix and Other Special Transitionssupporting

confidence: 73%

Codimension-2 surfaces and their Hilbert spaces: low-energy clues for holography from general covariance

Neiman¹

2009

Class. Quantum Grav.

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We argue that the holographic principle may be hinted at already from low-energy considerations, assuming diffeomorphism invariance, quantum mechanics and Minkowski-like causality. We consider the states of finite spacelike hypersurfaces in a diffeomorphism-invariant QFT. A low-energy regularization is assumed. We note a natural dependence of the Hilbert space on a codimension-2 boundary surface. The Hilbert product is defined dynamically, in terms of transition amplitudes which are described by a path integral. We show that a canonical basis is incompatible with these assumptions, which opens the possibility for a smaller Hilbert-space dimension than canonically expected. We argue further that this dimension may decrease with surface area at constant volume, hinting at holographic area-proportionality. We draw comparisons with other approaches and setups, and propose an interpretation for the non-holographic space of graviton states at asymptotically-Minkowski null infinity.

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Section: The S-matrix and Other Special Transitionssupporting

confidence: 73%

Codimension-2 surfaces and their Hilbert spaces: low-energy clues for holography from general covariance

Neiman¹

2009

Class. Quantum Grav.

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“…After canonical quantization, the corresponding charge operators form (4n + D)-dimensional Poincaré-like superalgebra IOSp(2n + D, 2n). 17,13,14 The existence of this remarkable symmetry justifies the assertion that b ρ , but not bρ , should be regarded as the primary field. Now, we proceed to considering the two-dimensional case n = 2.…”

Section: Exact Treatmentmentioning

confidence: 72%

“…and "angular supermomentum" 17,13,14 The existence of this remarkable symmetry justifies the assertion that b ρ , but notb ρ , should be regarded as the primary field. Now, we proceed to considering the two-dimensional case n = 2.…”

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confidence: 63%

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Question on D=26: String Theory Versus Quantum Gravity

Abe

Nakanishi²

1998

Int. J. Mod. Phys. A

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In the covariant-gauge two-dimensional quantum gravity, various derivations of the critical dimension D = 26 of the bosonic string are critically reviewed, and their interrelations are clarified. It is shown that the string theory is not identical with the proper framework of the two-dimensional quantum gravity, but the former should be regarded as a particular aspect of the latter. The appearance of various anomalies is shown to be explainable in terms of a new type of anomaly in a unified way. *

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“…Now, we present a brief summary of the manifestly-covariant canonical operator formalism of the quantum Einstein gravity based on the BRS invariance. 2,3 Here, the BRS invariance is the quantum version of the local-translation (i.e., generalcoordinate transformation) invariance; since the arbitrary transformation function in the classical Einstein gravity is replaced by the local-translation FP ghost, any local-translationally invariant (in the classical sense) quantity is invariant under the BRS transformation of the quantum Einstein gravity.…”

Section: Quantum Einstein Gravitymentioning

confidence: 99%

Quantum-theoretical origin of the Lorentz invariance of the elementary-particle theory

Nakanishi

2014

Int. J. Mod. Phys. A

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The reason why the elementary-particle theory must be Lorentz invariant is investigated under the principle of quantum priority, which implies that the existence of any space–time manifold such as the Minkowski space should not be assumed logically prior to the formulation of quantum-theoretical framework. The consideration is based on the canonical operator formalism of quantum Einstein gravity, which is formulated without introducing any classical background space–time nor any particular metric signature. The Lorentz invariance of the elementary-particle theory is derived as a consequence of the spontaneous breakdown of general linear invariance on the basis of quantum Einstein gravity. The pseudo-Riemannian space–time can appear not as a consequence of the presence of gravitation, but as that of the spontaneous breakdown of translational invariance.

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Manifestly Covariant Canonical Formalism of Quantum Gravity - Systematic Presentation of the Theory

Cited by 17 publications

References 46 publications

Codimension-2 surfaces and their Hilbert spaces: low-energy clues for holography from general covariance

Codimension-2 surfaces and their Hilbert spaces: low-energy clues for holography from general covariance

Question on D=26: String Theory Versus Quantum Gravity

Quantum-theoretical origin of the Lorentz invariance of the elementary-particle theory

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