Develops a matrix-free SRQ-based action for the AL volume operator that exactly preserves the kernel and supports large-scale Monte Carlo and spectral estimates without dense matrices.
Introduction to Modern Canonical Quantum General Relativity
7 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the fact that the quantum theory is based on formulating classical general relativity as a theory of connections rather than metrics as compared to in original version due to Arnowitt, Deser and Misner. Canonical quantum general relativity is an attempt to define a mathematically rigorous, non-perturbative, background independent theory of Lorentzian quantum gravity in four spacetime dimensions in the continuum. The approach is minimal in that one simply analyzes the logical consequences of combining the principles of general relativity with the principles of quantum mechanics. The requirement to preserve background independence has lead to new, fascinating mathematical structures which one does not see in perturbative approaches, e.g. a fundamental discreteness of spacetime seems to be a prediction of the theory providing a first substantial evidence for a theory in which the gravitational field acts as a natural UV cut-off. An effort has been made to provide a self-contained exposition of a restricted amount of material at the appropriate level of rigour which at the same time is accessible to graduate students with only basic knowledge of general relativity and quantum field theory on Minkowski space.
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Fractional gravity yields stable de Sitter expansion and exact bouncing solutions driven by phantom (w < -1) or ghost (negative energy) fluids, with results independent of the form-factor representation.
Variational minimization of the squared Hamiltonian constraint in a truncated one-vertex loop gravity model yields three classes of near-kernel states; one factorized branch matches reduced Thiemann coherent states with high fidelity.
Loop quantum cosmology models harbor physical singularities or inconsistent space-time structures, with a new effective Friedmann equation revealing a sub-Planckian bounce after a singularity at infinite scale factor resembling a time-reversed big rip.
Extends quantum Oppenheimer-Snyder collapse model to higher dimensions plus cosmological constant and reports modified AdS black-hole thermodynamics with finite small-black-hole temperature and an extra quantum-induced phase transition.
In a path-integral model of timeless quantum systems, time evolution arises when a clock is prepared in a semiclassical state, showing that the cosine problem in quantum gravity follows from time-reversal invariance and neutral boundary conditions.
A van der Waals-inspired modification to general relativity renders the gravitational coupling dynamical, providing a mechanism to avoid Big Bang and black hole singularities.
citing papers explorer
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A matrix free action of the Ashtekar-Lewandowski volume operator of loop quantum gravity
Develops a matrix-free SRQ-based action for the AL volume operator that exactly preserves the kernel and supports large-scale Monte Carlo and spectral estimates without dense matrices.
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Cosmology of fractional gravity
Fractional gravity yields stable de Sitter expansion and exact bouncing solutions driven by phantom (w < -1) or ghost (negative energy) fluids, with results independent of the form-factor representation.
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Emergent Thiemann coherent states in the near-kernel sector of quantum reduced loop gravity
Variational minimization of the squared Hamiltonian constraint in a truncated one-vertex loop gravity model yields three classes of near-kernel states; one factorized branch matches reduced Thiemann coherent states with high fidelity.
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Singularities in loop quantum cosmology
Loop quantum cosmology models harbor physical singularities or inconsistent space-time structures, with a new effective Friedmann equation revealing a sub-Planckian bounce after a singularity at infinite scale factor resembling a time-reversed big rip.
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Higher-dimensional quantum-corrected Oppenheimer-Snyder model with a cosmological constant
Extends quantum Oppenheimer-Snyder collapse model to higher dimensions plus cosmological constant and reports modified AdS black-hole thermodynamics with finite small-black-hole temperature and an extra quantum-induced phase transition.
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The problem of time: a path integral view
In a path-integral model of timeless quantum systems, time evolution arises when a clock is prepared in a semiclassical state, showing that the cosine problem in quantum gravity follows from time-reversal invariance and neutral boundary conditions.
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Van der Waals Gravity Theory
A van der Waals-inspired modification to general relativity renders the gravitational coupling dynamical, providing a mechanism to avoid Big Bang and black hole singularities.