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Within the second half of the last century, quantum cosmology concretely became one of the main research lines within gravitational theory and cosmology. Substantial progress has been made. Furthermore, quantum cosmology can become a domain that will gradually develop further over the next handful of decades, perhaps assisted by technological developments. Indications for new physics (i.e., beyond the standard model of particle physics or general relativity) could emerge and then the observable universe would surely be seen from quite a new perspective. This motivates bringing quantum cosmology to more research groups and individuals.This Special Issue (SI) aims to provide a wide set of reviews, ranging from foundational issues to (very) recent advancing discussions. Concretely, we want to inspire new work proposing observational tests, providing an aggregated set of contributions, covering several lines, some of which are thoroughly explored, some allowing progress, and others much unexplored. The aim of this SI is motivate new researchers to employ and further develop quantum cosmology over the forthcoming decades. Textbooks and reviews exist on the present subject, and this SI will complementarily assist in offering open access to a set of wide-ranging reviews. Hopefully, this will assist new interested researchers, in having a single open access online volume, with reviews that can help. In particular, this will help in selecting what to explore, what to read in more detail, where to proceed, and what to investigate further within quantum cosmology.

string cosmology --- quantum cosmology --- Wheeler-DeWitt equation --- loop quantum cosmology --- observations --- classical and quantum cosmology --- time --- quantum fields in curved spacetime --- Brans–Dicke theory --- bounce models --- de Broglie–Bohm interpretation --- quantum geometrodynamics --- extended theories of gravity --- dark energy singularities --- quantum gravity --- Hawking radiation --- entanglement entropy --- uniqueness of the quantization --- polymer quantum mechanics --- bounce --- no-boundary proposal --- instantons --- multiverse --- superspace --- third quantisation --- universe–antiuniverse pair --- weyl curvature hypothesis --- early universe cosmology --- singularity and bounce --- cyclic universe --- quantum fields --- backreaction effects --- supersymmetry --- noncommutativity --- generalized uncertainty principles --- canonical quantum gravity --- clocks --- noether symmetries --- ADM formalism --- exact solutions --- supersymmetric quantum mechanics --- shape invariant potentials --- supersymmetric quantum cosmology --- n/a --- Brans-Dicke theory --- de Broglie-Bohm interpretation --- universe-antiuniverse pair

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This book celebrates the 80 years of the Professor Eugene P. Wigner paper “On Unitary Representations of the Inhomogeneous Lorentz Group", published in The Annals of Mathematics in 1939. We have collected several contributions divided into Research articles and Reviews. All contributions are technical, but the papers also bring a health element of didactic. Practitioners from several areas, from Gravity to Quantum Field Theory and Quantum Mechanics, as well as students, shall find a rich material in this Volume.

spinors in 4d --- regularization --- anomalies --- quantum gravity --- quantum mechanics --- symmetry --- quantum cosmology --- special relativity --- combination of velocities --- wigner angle --- quaternions --- gauge field theory --- Yang-Mills fields --- modified gravity --- non-Riemannian geometry --- spacetime symmetries --- gauge field theories --- gauge anomalies --- nonperturbative techniques --- ray representation --- strongly continuous --- continuity --- Hilbert space --- entanglement --- bispinors --- chirality --- n/a

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"The four volumes of the proceedings of MG14 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 35 morning plenary talks over 6 days, 6 evening popular talks and 100 parallel sessions on 84 topics over 4 afternoons. Volume A contains plenary and review talks ranging from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. The remaining volumes include parallel sessions which touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational wave detectors and data analysis, precision gravitational measurements, loop quantum gravity, quantum cosmology, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity"--

Binary Systems --- Astrophysics --- Loop Quantum Gravity --- Gravitational Wave Detectors and Data Analysis --- Black Hole Thermodynamics --- Active Galactic Nuclei --- Observational Cosmology --- Gravitational Wave --- X-ray Sources --- Dark Matter --- General Relativity --- Cosmic Rays --- Inflation --- Numerical Relativity --- Neutrinos --- Theoretical Physics --- Large Scale Structure --- Inhomogeneous Cosmology --- Radiative Transfer --- Supernova --- Gravitation --- Black Hole --- White Dwarf --- Precision Gravitational Measurements --- Quantum Gravity --- Quantum Cosmology --- Einstein-Maxwell Systems --- String Theory --- Cosmic Microwave Background Anisotropies --- Accretion Disks --- Neutron Star --- Gravitational Lensing --- Exact Solutions of Einstein's Equations --- Early Universe Models --- Wormholes --- Cosmology --- Pulsar --- Gamma Ray Burst