Sidney Coleman (1937-2007) earned his doctorate at Caltech under Murray Gell-Mann. Before completing his thesis, he was hired by Harvard and remained there his entire career. A celebrated particle theorist, he is perhaps best known for his brilliant lectures, given at Harvard and in a series of summer school courses at Erice, Sicily. Three times in the 1960s he taught a graduate course on Special and General Relativity; this book is based on lecture notes taken by three of his students and compiled by the Editors.

Three eminent scientists, each well known for the clarity of their writing, present for students and researchers what is known about the internal structure, origin and evolution of White Dwarfs, Neutron Stars and Black Holes, all objects at the final stage of stellar evolution. They cover fascinating topics such as pulsation of white dwarfs, millisecond pulsars or the dynamics around black holes. The book is written for graduate students in astrophysics, but is also of interest to professional astronomers and physicists.

This book provides a completely revised and expanded version of the previous classic edition 'General Relativity and Relativistic Astrophysics'. In Part I the foundations of general relativity are thoroughly developed, while Part II is devoted to tests of general relativity and many of its applications. Binary pulsars - our best laboratories for general relativity - are studied in considerable detail. An introduction to gravitational lensing theory is included as well, so as to make the current literature on the subject accessible to readers. Considerable attention is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerr solution, Israel's proof of his uniqueness theorem, and a derivation of the basic laws of black hole physics. Part II ends with Witten's proof of the positive energy theorem, which is presented in detail, together with the required tools on spin structures and spinor analysis. In Part III, all of the differential geometric tools required are developed in detail. A great deal of effort went into refining and improving the text for the new edition. New material has been added, including a chapter on cosmology. The book addresses undergraduate and graduate students in physics, astrophysics and mathematics. It utilizes a very well structured approach, which should help it continue to be a standard work for a modern treatment of gravitational physics. The clear presentation of differential geometry also makes it useful for work on string theory and other fields of physics, classical as well as quantum.

This textbook is designed to serve as a link between the basic disciplines of physics and the frontier topics within high energy astrophysics, aiming at a level of difficulty congruent with that of other physics topics studied at undergraduate level. Therefore, this preparatory and introductory text serves as a gateway to a more detailed study of many of the most interesting and complex phenomena being investigated by contemporary astrophysics. Among others, these include: the evolution of stars, supernovae, neutron stars, black holes, solar neutrinos, and - importantly - the exciting new field of gravitational wave astronomy. The book is supplemented by a collection of problems with which students can test their understanding of the material presented.

The ultimate proofs that black holes exist have been obtained very recently thanks to the detection of gravitational waves from their coalescence and due to material orbiting at a distance of some gravitational radii imaged by optical interferometry or X-ray reverberation mapping. This book provides three comprehensive and up-to-date reviews covering the gravitational wave breakthrough, our understanding of accretion and feedback in supermassive black holes and the relevance of black holes for the Universe since the Big Bang. Neil J. Cornish presents gravitational wave emission from black hole mergers and the physics of detection. Andrew King reviews the physics of accretion on to supermassive black holes and their feedback on host galaxies. Tiziana Di Matteo addresses our understanding of black hole formation at cosmic dawn, the emergence of the first quasars, black hole merging and structure formation. The topics covered by the 48th Saas-Fee Course provide a broad overview of the importance of black holes in modern astrophysics.

The wealth of recent cosmic microwave background and large-scale structure data has transformed the field of cosmology. These observations have not only become precise enough to answer questions about the universe on the largest scales, but also to address puzzles in the microscopic description of Nature. This thesis investigates new ways of probing the early universe, the properties of neutrinos and the possible existence of other light particles. In particular, based on detailed theoretical insights and novel analyses, new evidence for the cosmic neutrino background is found in the distribution of galaxies and in cosmic microwave background data. This tests the Standard Model of particle physics and the universe back to a time when it was about one second old. Furthermore, it is demonstrated that future observations will be capable of probing physics beyond the Standard Model since they can achieve a particular target which would either allow the detection of any light particles that have ever been in thermal equilibrium or imply strong bounds on their properties.

"If a child wants proof, we can think of 10 different ways to show that we are surrounded by air, but we are, of course, normally unaware that we live at the bottom of an 'ocean" of air. It is claimed, in this book, that we are unaware, similarly, that we are surrounded by an atmosphere of aether. There is one major difference, however: We have not been able to detect the aether.Nevertheless, the aether provides a solution to the following mystery: How can light, or any electromagnetic wave, travel for billions of years across the vastness of the Universe, without losing any energy? The answer is that the Universe is filled with a light-transmitting medium, The Aether. The proof that there is an aether is the subject of the present book."

This thesis uses the tools of quantum information science to uncover fascinating new insights about the intersection of quantum theory and relativity. It is divided into three self-contained parts, the first of which employs detector models to investigate how the information content of quantum fields depends on spacetime curvature and global spacetime topology. The behavior of Unruh-DeWitt detectors on curved spacetimes are investigated, following which these detectors are used to probe the vacuum state of a scalar field in various topologies. This leads to a generalization of the entanglement harvesting protocol involving detectors in arbitrary curved spacetimes admitting a Wightman function. The second part extends the theory of quantum reference frames to those associated with noncompact groups. Motivated by the pursuit of a relational relativistic quantum theory where the group of reference frames is the Poincare group, the author then generalizes a communication protocol between two parties lacking a common reference frame to the scenario where the group of transformations of their reference frame is a one-dimensional noncompact Lie group. Finally, the third part, inspired by theories of quantum gravity, generalizes the conditional probability interpretation of time, a proposed mechanism for time to emerge from a fundamentally timeless Universe. While the conditional probability interpretation of time is based upon conditioning a solution to the Wheeler-DeWitt equation on a subsystem of the universe that acts a clock, the author extends this approach to include an interaction between the system being used as a clock and a system whose evolution the clock is tracking.

In order to outline possible future directions in galaxy research, this book wants to be a short stopover, a moment of self-reflection of the past century of achievements in this area. Since the pioneering years of galaxy research in the early 20th century, the research on galaxies has seen a relentless advance directly connected to the parallel exponential growth of new technologies. Through a series of interviews with distinguished astronomers the editors provide a snapshot of the achievements obtained in understanding galaxies. While many initial questions about their nature have been addressed, many are still open and require new efforts to achieve a solution. The discussions may reveal paradigms worthwhile revisiting. With the help of some of those scientists who have contributed to it, the editors sketch the history of this scientific journey and ask them for inspirations for future directions of galaxy research.

The three neutrinos are ghostly elementary particles that exist all across the Universe. Though every second billions of them fly through us, they are extremely hard to detect. We used to think they had no mass, but recently discovered that in fact they have a tiny mass. The quest for the neutrino mass scale and mass ordering (specifying how the three masses are distributed) is an extremely exciting one, and will open the door towards new physics operating at energy scales we can only ever dream of reaching on Earth. This thesis explores the use of measurements of the Cosmic Microwave Background (the oldest light reaching us, a snapshot of the infant Universe) and maps of millions of galaxies to go after the neutrino mass scale and mass ordering. Neutrinos might teach us something about the mysterious dark energy powering the accelerated expansion of the Universe, or about cosmic inflation, which seeded the initial conditions for the Universe. Though extremely baffling, neutrinos are also an exceptionally exciting area of research, and cosmological observations promise to reveal a great deal about these elusive particles in the coming years.

Due to steadily improving experimental accuracy, relativistic concepts - based on Einstein's theory of Special and General Relativity - are playing an increasingly important role in modern geodesy. This book offers an introduction to the emerging field of relativistic geodesy, and covers topics ranging from the description of clocks and test bodies, to time and frequency measurements, to current and future observations. Emphasis is placed on geodetically relevant definitions and fundamental methods in the context of Einstein's theory (e.g. the role of observers, use of clocks, definition of reference systems and the geoid, use of relativistic approximation schemes). Further, the applications discussed range from chronometric and gradiometric determinations of the gravitational field, to the latest (satellite) experiments. The impact of choices made at a fundamental theoretical level on the interpretation of measurements and the planning of future experiments is also highlighted. Providing an up-to-the-minute status report on the respective topics discussed, the book will not only benefit experts, but will also serve as a guide for students with a background in either geodesy or gravitational physics who are interested in entering and exploring this emerging field.

Our vast Universe is filled with an enormous amount of matter and energy, which are the source of large gravitational potentials affecting all physical phenomena. Because this fact about the size and contents of the Universe was not known when our fundamental theories of dynamics and relativity were completed by the 1920s, the current theories - based as they are in empty space - fail to incorporate cosmic gravity. Though the current theories are consistent with the majority of empirical facts, there are some crucial discrepancies, which demand a drastic shift to a cosmic gravitational paradigm for the theories of relativity and dynamics. The book is a detailed and widely accessible account of this paradigm, called Cosmic Relativity, supported by ample empirical evidence. It is established that all motional relativistic effects are cosmic gravitational effects. The new theory of Cosmic Relativity solves and answers all outstanding questions and puzzles about dynamics and relativity.

Astrophysical observations implying the existence of Dark Matter and Dark Energy, which are not described by the Standard Model (SM) of particle physics, have led to extensions of the SM predicting new particles that could be directly produced at the Large Hadron Collider (LHC) at CERN. Based on 2015 and 2016 ATLAS proton-proton collision data, this thesis presents searches for the supersymmetric partner of the top quark, for Dark Matter, and for DarkEnergy, in signatures with jets and missing transverse energy. Muon detection is key to some of the most important LHC physics results, including the discovery of the Higgs boson and the measurement of its properties. The efficiency with which muons can be detected with the ATLAS detector is measured using Z boson decays. The performance of high-precision Monitored Drift Tube muon chambers under background rates similar to the ones expected for the High Luminosity-LHC is studied.

This book offers an overview of the fundamental dynamical processes, which are necessary to understand astrophysical phenomena, from the viewpoint of hydrodynamics, magnetohydrodynamics, and radiation hydrodynamics. The book consists of three parts: The first discusses the fundamentals of hydrodynamics necessary to understand the dynamics of astrophysical objects such as stars, interstellar gases and accretion disks. The second part reviews the interactions between gases and magnetic fields on fluid motions - the magnetohydrodynamics - highlighting the important role of magnetic fields in dynamical phenomena under astrophysical environments. The third part focuses on radiation hydrodynamics, introducing the hydrodynamic phenomena characterized by the coupling of radiation and gas motions and further on relativistic radiation hydrodynamics. Intended as a pedagogical introduction for advanced undergraduate and graduate students, it also provides comprehensive coverage of the fundamentals of astrophysical fluid dynamics, making it an effective resource not only for graduate courses, but also for beginners wanting to learn about hydrodynamics, magnetohydrodynamics, and radiation hydrodynamics in astrophysics independently.

This book offers an introduction to statistical mechanics, special relativity, and quantum physics. It is based on the lecture notes prepared for the one-semester course of "Quantum Physics" belonging to the Bachelor of Science in Material Sciences at the University of Padova. The first chapter briefly reviews the ideas of classical statistical mechanics introduced by James Clerk Maxwell, Ludwig Boltzmann, Willard Gibbs, and others. The second chapter is devoted to the special relativity of Albert Einstein. In the third chapter, it is historically analyzed the quantization of light due to Max Planck and Albert Einstein, while the fourth chapter discusses the Niels Bohr quantization of the energy levels and the electromagnetic transitions. The fifth chapter investigates the Schrodinger equation, which was obtained by Erwin Schrodinger from the idea of Louis De Broglie to associate to each particle a quantum wavelength. Chapter Six describes the basic axioms of quantum mechanics, which were formulated in the seminal books of Paul Dirac and John von Neumann. In chapter seven, there are several important application of quantum mechanics: the quantum particle in a box, the quantum particle in the harmonic potential, the quantum tunneling, the stationary perturbation theory, and the time-dependent perturbation theory. Chapter Eight is devoted to the study of quantum atomic physics with special emphasis on the spin of the electron, which needs the Dirac equation for a rigorous theoretical justification. In the ninth chapter, it is explained the quantum mechanics of many identical particles at zero temperature, while in Chapter Ten the discussion is extended to many quantum particles at finite temperature by introducing and using the quantum statistical mechanics. The four appendices on Dirac delta function, complex numbers, Fourier transform, and differential equations are a useful mathematical aid for the reader.

In this third volume of three, quantum electrodynamics is formulated in the language of physical "dressed" particles. A theory where charged particles interact via instantaneous action-at-a-distance forces is constructed - without need for renormalization. This theory describes electromagnetic phenomena in terms of directly interacting charges, but in full accord with fundamental principles of relativity and causality. Contents Three ways to look at QFT Dressing What are advantages of dressed Hamiltonian? Coulomb potential and beyond Decays RQD in higher orders Classical electrodynamics Experimental support of RQD Particles and relativity Special theory of relativity Unitary dressing transformation Integral for decay law Coulomb scattering integral in fourth order Relativistic invariance of Coulomb-Darwin-Breit electrodynamics

This second volume of three on relativistic quantum theories of interacting charged particles discusses quantum theories of systems with variable numbers of particles. Basics of the Fock space and quantum electrodynamics are covered with an emphasis on renormalization. In contrast to the usual treatment of the topic, particles (rather than fields) are chosen as basic ingredients. Contents Fock space Scattering in Fock space Quantum electrodynamics Renormalization Useful integrals Quantum fields of fermions Quantum field of photons QED interaction in terms of particle operators Relativistic invariance of QFT Loop integrals in QED Scattering matrix in (v/c)2 approximation Checks of physical dimensions

This book introduces notation, terminology, and basic ideas of relativistic quantum theories. The discussion proceeds systematically from the principle of relativity and postulates of quantum logics to the construction of Poincare invariant few-particle models of interaction and scattering. It is the first of three volumes formulating a consistent relativistic quantum theory of interacting charged particles. Contents Quantum logic Poincare group Quantum mechanics and relativity Observables Elementary particles Interaction Scattering Delta function Groups and vector spaces Group of rotations Lie groups and Lie algebras Hilbert space Operators Subspaces and projections Representations of groups and algebras Pseudo-orthogonal representation of Lorentz group

This book delves into finite mathematics and its application in physics, particularly quantum theory. It is shown that quantum theory based on finite mathematics is more general than standard quantum theory, whilst finite mathematics is itself more general than standard mathematics.As a consequence, the mathematics describing nature at the most fundamental level involves only a finite number of numbers while the notions of limit, infinite/infinitesimal and continuity are needed only in calculations that describe nature approximately. It is also shown that the concepts of particle and antiparticle are likewise approximate notions, valid only in special situations, and that the electric charge and baryon- and lepton quantum numbers can be only approximately conserved.

The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spacetime cannot be fundamentally correct. Hence there should exist a broader theory comprising both in appropriate limits, i.e., quantum gravity. This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity. These issues relate to fundamental questions concerning the various formalisms of quantization; specific questions concerning concrete processes, like gravitational collapse or black-hole evaporation; and the all important question concerning the possibility of experimental tests of quantum-gravity effects.

These peer-reviewed NIC XV conference proceedings present the latest major advances in nuclear physics, astrophysics, astronomy, cosmochemistry and neutrino physics, which provide the necessary framework for a microscopic understanding of astrophysical processes. The book also discusses future directions and perspectives in the various fields of nuclear astrophysics research. In addition, it also includes a limited number of section of more general interest on double beta decay and dark matter.

Albert Einstein, one of the most prolific scientists of the twentieth century, developed the theory of relativity which was crucial for the advancement of modern physics. Young Einstein identified a paradox between Newtonian Mechanics and Maxwell's equations which pointed to a flawed understanding of space and time by the scientists of the day. In Relativity, Einstein presents his findings using a minimal amount of mathematical language, but the text can still be challenging for readers who lack an extensive scientific background. The Routledge Guidebook to Einstein's Relativity expands on and supplements this seminal text, by exploring: the historical context of Einstein's work and the background to his breakthroughs details of experimental verification of special and general relativity the enduring legacy of Einstein's theories and their implications for future scientific breakthroughs. This is an essential introduction for students of physics, philosophy and history in understanding the key elements of the work and the importance of this classic text to society today.

This thesis studies various aspects of non-critical strings both as an example of a non-trivial and solvable model of quantum gravity and as a consistent approximation to the confining flux tube in quantum chromodynamics (QCD). It proposes and develops a new technique for calculating the finite volume spectrum of confining flux tubes. This technique is based on approximate integrability and it played a game-changing role in the study of confining strings. Previously, a theoretical interpretation of available high quality lattice data was impossible, because the conventional perturbative expansion for calculating the string spectra was badly asymptotically diverging in the regime accessible on the lattice. With the new approach, energy levels can be calculated for much shorter flux tubes than was previously possible, allowing for a quantitative comparison with existing lattice data. The improved theoretical control makes it manifest that existing lattice data provides strong evidence for a new pseudoscalar particle localized on the QCD fluxtube - the worldsheet axion. The new technique paves a novel and promising path towards understanding the dynamics of quark confinement.