New formulation of Horava–Lifshitz quantum gravity as a master constraint theory

Soo, Chopin; Yang, Jinsong; Yu, Hoi-Lai

doi:10.1016/j.physletb.2011.05.055

“…(9)). In particular, by (10) and (11), proper time intervals measured by physical clocks in spacetimes that are solutions of Einstein's equations always agree with the result of Eq. (12).…”

Section: Paradigm Shift and Resolution Of The Problem Of Timementioning

confidence: 57%

General Relativity Without Paradigm of Space-Time Covariance: Sensible Quantum Gravity and Resolution of the “Problem of Time”

Soo

¹

,

Yu

²

2013

Towards Ultimate Understanding of the Universe

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The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full spacetime covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical structure, yield transparent physical dynamics and a resolution of the problem of time. The deep divide between quantum mechanics and conventional canonical formulations of quantum gravity is overcome with a Schrödinger equation for quantum geometrodynamics that describes evolution in intrinsic time. Unitary time development with gaugeinvariant temporal ordering is also viable. All Kuchar observables become physical; and classical spacetime, with direct correlation between its proper times and intrinsic time intervals, emerges from constructive interference. The framework not only yields a physical Hamiltonian for Einstein's theory, but also prompts natural extensions and improvements towards a well behaved quantum theory of gravity. It is a consistent canonical scheme to discuss Horava-Lifshitz theories with intrinsic time evolution, and of the many possible alternatives that respect 3-covariance (rather than the more restrictive 4-covariance of Einstein's theory), Horava's "detailed balance" form of the Hamiltonian constraint is essentially pinned down by this framework. Issues in quantum gravity that depend on radiative corrections and the rigorous definition and regularization of the Hamiltonian operator are not addressed in this work.

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“…In loop quantum gravity, the non-perturbative master constraint program [9] seeks representations not of the Dirac algebra, but of the master constraint algebra which has the advantages of having structure constants (rather than functions), and of decoupling the equivalent quantum Hamiltonian constraint from spatial diffeomorphism generators H i . Reference [10] consistently realized Horava gravity theories as canonical theories with first-class master constraint algebra. This not only removes the canonical inconsistencies of projectable Horava theory, but also captures the essence of the theory in retaining spatial diffeomorphisms as the only local gauge symmetries.…”

Section: Introduction and Overviewmentioning

confidence: 99%

General Relativity without paradigm of space-time covariance, and resolution of the problem of time

Soo

¹

,

Yu

²

2014

Progress of Theoretical and Experimental Physics

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The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full spacetime covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical structure, yield transparent physical dynamics and a resolution of the problem of time. The deep divide between quantum mechanics and conventional canonical formulations of quantum gravity is overcome with a Schrödinger equation for quantum geometrodynamics that describes evolution in intrinsic time. Unitary time development with gaugeinvariant temporal ordering is also viable. All Kuchar observables become physical; and classical spacetime, with direct correlation between its proper times and intrinsic time intervals, emerges from constructive interference. The framework not only yields a physical Hamiltonian for Einstein's theory, but also prompts natural extensions and improvements towards a well behaved quantum theory of gravity. It is a consistent canonical scheme to discuss Horava-Lifshitz theories with intrinsic time evolution, and of the many possible alternatives that respect 3-covariance (rather than the more restrictive 4-covariance of Einstein's theory), Horava's "detailed balance" form of the Hamiltonian constraint is essentially pinned down by this framework. Issues in quantum gravity that depend on radiative corrections and the rigorous definition and regularization of the Hamiltonian operator are not addressed in this work.

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Symmetry breaking and restoration in Lifshitz type theories

Farakos¹,

Metaxas²

2012

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We consider the one-loop effective potential at zero and finite temperature in scalar field theories with anisotropic space-time scaling. For $z=2$, there is a symmetry breaking term induced at one-loop at zero temperature and we find symmetry restoration through a first-order phase transition at high temperature. For $z=3$, we considered at first the case with a positive mass term at tree level and found no symmetry breaking effects induced at one-loop, and then we study the case with a negative mass term at tree level where we cannot conclude about symmetry restoration effects at high temperature because of the imaginary parts that appear in the effective potential for small values of the scalar field.Comment: 11 pages, 2 figures, version accepted in Physics Letters

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New formulation of Horava–Lifshitz quantum gravity as a master constraint theory

Cited by 5 publications

References 22 publications

General Relativity Without Paradigm of Space-Time Covariance: Sensible Quantum Gravity and Resolution of the “Problem of Time”

General Relativity Without Paradigm of Space-Time Covariance: Sensible Quantum Gravity and Resolution of the “Problem of Time”

General Relativity without paradigm of space-time covariance, and resolution of the problem of time

Symmetry breaking and restoration in Lifshitz type theories

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