Regularization of the cosmological sector of loop quantum gravity with bosonic matter and the related problems with general covariance of quantum corrections
arXiv:2001.04491 · doi:10.1103/PhysRevD.103.046008
Abstract
This article concerns the problems regarding different lattice regularization techniques for the matter fields of Hamiltonian constraints defined in the framework of loop quantum gravity. The analysis is formulated in the phase space-reduced cosmological model of the hypothetical theory of canonical quantum general relativity. This article explains why a different than links-related lattice smearing of fields leads to a local violation of general covariance. This happens by assuming, for instance, the nodes-related smearing. Therefore, this problem occurs in the case of any polymerlike scalar field quantization method by breaking the background independence of the semiclassical predictions. In consequence, the diffeomorphism symmetry that depends on a links distribution is broken locally at the level of generally relativistic corrections. Moreover, by using the phase space-reduced gauge fixing technique to analyze this issue, the results are general and they concern any coupling with the links-regularized gravitational degrees of freedom in loop quantum gravity. Therefore, they lead to the following no-go conclusion. Any lattice smearing of matter, not defined by using the geometrical distribution specified by the links-fluxes duality, violates the general principle of relativity.
arXiv comment24 pages, 4 figures, essentially improved methodology leading to a no-go conclusion, version accepted by Physical Review D
References in corpus (45)
- The Dynamics of General Relativity
- Loop Quantum Cosmology: A Status Report
- Absence of Singularity in Loop Quantum Cosmology
- Real Ashtekar Variables for Lorentzian Signature Space-times
- Quantum Spin Dynamics (QSD)
- QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories
- Loop quantum cosmology of Bianchi I models
- Quantum gravity, shadow states, and quantum mechanics
- Quantum Spin Dynamics (QSD) II
- Gauge Field Theory Coherent States (GCS) : I. General Properties
- An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era
- Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
- The Inverse Scale Factor in Isotropic Quantum Geometry
- Kinematical Hilbert Spaces for Fermionic and Higgs Quantum Field Theories
- QSD III : Quantum Constraint Algebra and Physical Scalar Product in Quantum General Relativity
- Alternative quantization of the Hamiltonian in loop quantum cosmology II: Including the Lorentz term
- Hybrid quantization of an inflationary universe
- Gauge Field Theory Coherent States (GCS) : III. Ehrenfest Theorems
- Quantum field theory on a cosmological, quantum space-time
- Loop Quantum Cosmology I: Kinematics
- Polymer and Fock representations for a Scalar field
- Quantum-Reduced Loop Gravity: Cosmology
- Observational issues in loop quantum cosmology
- Background independent quantization and the uncertainty principle
- Critical evaluation of common claims in loop quantum cosmology
- Anomaly-free cosmological perturbations in effective canonical quantum gravity
- Cosmological perturbations in Hybrid Loop Quantum Cosmology: Mukhanov-Sasaki variables
- Canonical Gravity with Fermions
- Testing loop quantum cosmology
- Quantum Cosmology: Effective Theory
- A no-go result for covariance in models of loop quantum gravity
- Quantum Reduced Loop Gravity: Semiclassical limit
- Cosmological Coherent State Expectation Values in LQG I. Isotropic Kinematics
- Inverse volume corrections from loop quantum gravity and the primordial tensor power spectrum in slow-roll inflation
- Separate universes in loop quantum cosmology: framework and applications
- Non-covariance of the dressed-metric approach in loop quantum cosmology
- Background independent quantizations: the scalar field I
- Background independent quantizations: the scalar field II
- Dirac Fields in Loop Quantum Gravity and Big Bang Nucleosynthesis
- Quantum theory of electromagnetic fields in a cosmological quantum spacetime
- Quantum reduced loop gravity: extension to scalar field
- Quantum reduced loop gravity: extension to gauge vector field
- Critical Insight into the Cosmological Sector of Loop Quantum Gravity
- Implementation of the holonomy representation of the Ashtekar connection in loop quantum gravity
- Lie algebra of Ashtekar-Barbero connection operators