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Introduction to Modern Canonical Quantum General Relativity
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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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Cited by 9 Pith papers
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A matrix free action of the Ashtekar-Lewandowski volume operator of loop quantum gravity
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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 wi...
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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 ...
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Deep learning spinfoam vertex amplitudes: the Euclidean Barrett-Crane model
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A Minkowski-core black hole with cosmological constant and electric charge
A charged anti-de Sitter regular black hole with a Minkowski core is derived from a covariant effective Hamiltonian, and its thermodynamics show a phase transition that disappears above a critical value of the regular...
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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-induce...
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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 a...
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Echoes and quasinormal modes for static loop quantum black bounces
Scalar perturbations of the loop quantum black bounce spacetime produce echoes in traversable-wormhole configurations with a double-barrier effective potential, but not in regular-black-hole configurations with a sing...
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Shadows of rotating black holes in effective quantum gravity
For two covariant effective quantum gravity black holes, the quantum parameter ζ shrinks the shadow at moderate spin and creates a cuspy shadow edge near extremality.
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