This book focuses on a critical discussion of the status and prospects of current approaches in quantum mechanics and quantum field theory, in particular concerning gravity. It contains a carefully selected cross-section of lectures and discussions at the seventh conference “Progress and Visions in Quantum Theory in View of Gravity” which took place in fall 2018 at the Max Planck Institute for Mathematics in the Sciences in Leipzig. In contrast to usual proceeding volumes, instead of reporting on the most recent technical results, contributors were asked to discuss visions and new ideas in foundational physics, in particular concerning foundations of quantum field theory. A special focus has been put on the question of which physical principles of quantum (field) theory can be considered fundamental in view of gravity. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions of analysis on abstract Fock spaces (full Fock space, boson Fock space, fermion Fock space and boson-fermion Fock space). It includes the mathematics of second quantization, representation theory of canonical commutation and anti-commutation relations, Bogoliubov transformations, infinite-dimensional Dirac operators and supersymmetric quantum field in an abstract form. The second half of the book, Part II, covers applications of the mathematical theories in Part I to quantum field theory. Four kinds of free quantum fields are constructed and detailed analyses are made. A simple interacting quantum field model, called the van Hove-Miyatake model, is fully analyzed in an abstract form. Moreover, a list of interacting quantum field models is presented and an introductory description to each model is given. In this second edition, a new chapter (Chapter 15) is added to describe a mathematical theory of spontaneous symmetry breaking which is an important subject in modern quantum physics.This book is a good introductory text for graduate students in mathematics or physics who are interested in the mathematical aspects of quantum field theory. It is also well-suited for self-study, providing readers a firm foundation of knowledge and mathematical techniques for more advanced books and current research articles in the field of mathematical analysis on quantum fields. Numerous problems are added to aid readers in developing a deeper understanding of the field.

Physics and Astrophysics—Glimpses of the Progress provides a comprehensive account of physics and astrophysics from the time of Aristotle to the modern era of Stephen Hawking and beyond. It takes the readers of all ages through a pleasant journey touching on the major discoveries and inventions that have taken place in both the macro-world, including that in the cosmos, and the micro-world of atomic and subatomic particles related to physics and astrophysics. Use of historical perspective and anecdote makes the storytelling on the progress of physics and astrophysics both interesting and absorbing. While peering through different developments in these fields, the book never compromises with the sanctity of the scientific content, including the depth and beauty of the physical concept of the topics concerned and the philosophical viewpoints they represent. Where appropriate, the book also delves into value judgments of life that affect our civilization. Features The intricate concepts of physics and astrophysics are explained in simple terms and in easy-to-understand language. Physics and astrophysics are discussed in a connected and correlated way in a single volume of comprehensive size but in totality, which to date is the unique feature of this book. Starting with Aristotle’s Physics and going through the work of Newton, Einstein, Schrödinger, Hubble, Hewish, Hawking, and others, including the present research on dark energy, dark matter, and the fifth force of nature, the reader will be kept absorbed and spellbound. In addition to the fundamental principles of Newtonian mechanics, Einstein’s relativity, quantum mechanics, string theory, loop quantum gravity, and so on, the cutting-edge technologies of recent times, such as the Large Hadron Collider, Laser Interferometer Gravitational-wave Observatory, and Event Horizon Telescope, are also explored. The book is aimed primarily at undergraduate and graduate students, researchers, and professionals studying physics and astrophysics. General readers will also find the book useful to quench their thirst for knowledge about the developments in physics and astrophysics.

Black holes are one of the most fascinating predictions of general relativity. They are the natural product of the complete gravitational collapse of matter and today we have a body of observational evidence supporting the existence of black holes in the Universe. However, general relativity predicts that at the center of black holes there are spacetime singularities, where predictability is lost and standard physics breaks down. It is widely believed that spacetime singularities are a symptom of the limitations of general relativity and must be solved within a theory of quantum gravity. Since we do not have yet any mature and reliable candidate for a quantum gravity theory, researchers have studied toy-models of singularity-free black holes and of singularity-free gravitational collapses in order to explore possible implications of the yet unknown theory of quantum gravity. This book reviews all main models of regular black holes and non-singular gravitational collapses proposed in the literature, and discuss the theoretical and observational implications of these scenarios.

The proceedings of MG16 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 46 plenary presentations, 3 public lectures, 5 round tables and 81 parallel sessions arranged during the intense six-day online meeting. All talks were recorded and are available on the ICRANet YouTube channel at the following link: www.icranet.org/video_mg16.These proceedings are a representative sample of the very many contributions made at the meeting. They contain 383 papers, among which 14 come from the plenary sessions.The material represented in these proceedings cover the following topics: accretion, active galactic nuclei, alternative theories of gravity, black holes (theory, observations and experiments), binaries, boson stars, cosmic microwave background, cosmic strings, dark energy and large scale structure, dark matter, education, exact solutions, early universe, fundamental interactions and stellar evolution, fast transients, gravitational waves, high energy physics, history of relativity, neutron stars, precision tests, quantum gravity, strong fields, and white dwarf; all of them represented by a large number of contributions.The online e-proceedings are published in an open access format.

Aside from the obvious statement that it should be a theory capable of unifying general relativity and quantum field theory, not much is known about the true nature of quantum gravity. New ideas - and there are many of them for this is an exciting field of research - often diverge to a degree where it seems impossible to decide in which of the many possible direction(s) the ongoing developments should be further sustained. The division of the book in two (overlapping) parts reflects the duality between the physical vision and the mathematical construction. The former is represented by tutorial reviews on non-commutative geometry, on space-time discretization and renormalization and on gauge field path integrals. The latter one by lectures on cohomology, on stochastic geometry and on mathematical tools for the effective action in quantum gravity. The book will benefit everyone working or entering the field of quantum gravity research.

Main section headings: Ideas and Problems in Quantum Gravity; On Ellipticity and Quantum Gravity; Non-Local Boundary Data in Quantum Gravity; Non-Locality and Ellipticity for Gauge Theories; New Kernels in Quantum Gravity; Quantum Gravity from First Principles; Quantum Gravity and Spectral Geometry; Bibliography; Index.

'Written by young theoretical physicists who are experts in the field, this volume is meant both to provide an introduction to the field and to offer a review of the latest developments, not discussed in many other existing books, for senior researchers. It will also appeal to scientists who do not work directly on LQG but are interested in issues at the interface of general relativity and quantum physics.'CERN CourierThis volume presents a snapshot of the state-of-the-art in loop quantum gravity from the perspective of younger leading researchers. It takes the reader from the basics to recent advances, thereby bridging an important gap.The aim is two-fold — to provide a contemporary introduction to the entire field for students and post-docs, and to present an overview of the current status for more senior researchers. The contributions include the latest developments that are not discussed in existing books, particularly recent advances in quantum dynamics both in the Hamiltonian and sum over histories approaches; and applications to cosmology of the early universe and to the quantum aspects of black holes.

Our vision of God varies by culture. It has changed over the millennia. We no longer believe in the pagan gods of the Romans and Greeks. Why should we expect that our current view of God will not change? Scientific knowledge and discovery is occurring at a pace never before experienced in human history. Yet our concept of God remains mired in the 15th century. This is about to change. It will become increasingly difficult for religions to convince believers educated in modern science to blindly accept as truth religious dogmas conceived centuries ago. Religious scripture is a combination of literature, myth and superstition. Science will invalidate many of these myths. This is why intelligent design advocates fear science.