Closing the gaps in quantum space and time: Conformally augmented gauge structure of gravitation

Abstract

A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general relativity and scale-invariant scalar-tensor and dilaton theories. Consequently, matter to be coupled to such theories is restricted to be conformal or scale invariant. Standard model-type systems naturally fall into this category. The new loop quantization follows from a novel conformally generalized Holst action principle. In contrast to standard loop quantum gravity, the resulting quantum geometry is not beset by the Immirzi ambiguity and has no definitive area gaps within the considered large class of theories of gravitation. As an additional feature, the scale invariance gives rise to a conserved Weyl current and we discuss briefly its possible implication on the problem of time in quantum gravity.

arXiv comment35 pages (8 pages main text, 27 pages supplementary material); Published version

References in corpus (36)

• Discreteness of area and volume in quantum gravity
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• Loop Quantum Cosmology
• QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories
• Real and complex connections for canonical gravity
• Conformal Symmetry and the Standard Model
• Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
• The physical hamiltonian in nonperturbative quantum gravity
• Time and a physical Hamiltonian for quantum gravity
• Local Conformal Symmetry in Physics and Cosmology
• Black Holes in Loop Quantum Gravity
• Scale-Independent Inflation and Hierarchy Generation
• Loop quantum gravity: the first twenty five years
• Weyl Current, Scale-Invariant Inflation and Planck Scale Generation
• Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The slow-roll approximation
• Quantum gravitational decoherence of light and matter
• A short review on Noether's theorems, gauge symmetries and boundary terms
• Inflation in a scale invariant universe
• An alternative to the LCDM model: the case of scale invariance
• Fock representation of gravitational boundary modes and the discreteness of the area spectrum
• $BF$ gravity
• The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology
• The Thiemann Complexifier and the CVH algebra for Classical and Quantum FLRW Cosmology
• Loop Quantum Cosmology: A brief review
• Conformal geometrodynamics: True degrees of freedom in a truly canonical structure
• Loop quantum gravity coupled to a scalar field
• Unambiguous spin-gauge formulation of canonical general relativity with conformorphism invariance
• Quantum principle of sensing gravitational waves: From the zero-point fluctuations to the cosmological stochastic background of spacetime
• Quantum coherence, radiance, and resistance of gravitational systems
• Closing the gaps in quantum space and time: Conformally augmented gauge structure of gravitation
• Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity
• Scale Invariant Cosmology
• New 'phase' of quantum gravity
• Dynamical trapping and relaxation of scalar gravitational fields
• Conformal loop quantum gravity coupled to the Standard Model

Cited by in corpus (12)

• Alternative entropies and consistent black hole thermodynamics
• Big-bounce and future time singularity resolution in Bianchi I: the projective invariant Nieh-Yan case
• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• Inflation in Loop Quantum Cosmology
• Super-entropic black hole with Immirzi hair
• Generalized Ashtekar variables for Palatini f(R) models
• Closing the gaps in quantum space and time: Conformally augmented gauge structure of gravitation
• Decoding quantum gravity information with black hole accretion disk
• Quantization of time and the big bang via scale-invariant loop gravity
• Black holes quasinormal modes, Loop Quantum Gravity Immirzi parameter and nonextensive statistics
• Making a Quantum Universe: Symmetry and Gravity
• Bremsstrahlung of Light through Spontaneous Emission of Gravitational Waves