The purpose of this book is to illustrate some of the most important techniques which are helpful in combinatorial problems when computing quantum effects in covariant theories, like general relativity. In fact, most of the techniques find application also in broader contexts, such as low energy effective (chiral) Lagrangians or even in specific problems in condensed matter. Some of the topics covered are: the background field approach and the heat kernel ideas. The arguments are explained in some detail and the presentation is meant for young researchers and advanced students who are starting working in the field. As prerequisite the reader should have attended a course in quantum field theory including Feynman's path integral. In the Appendix a nontrivial calculation of one-loop divergences in Einstein-Hilbert gravity is explained step-by-step.

This concise textbook introduces the reader to advanced mathematical aspects of general relativity, covering topics like Penrose diagrams, causality theory, singularity theorems, the Cauchy problem for the Einstein equations, the positive mass theorem, and the laws of black hole thermodynamics. It emerged from lecture notes originally conceived for a one-semester course in Mathematical Relativity which has been taught at the Instituto Superior Tecnico (University of Lisbon, Portugal) since 2010 to Masters and Doctorate students in Mathematics and Physics. Mostly self-contained, and mathematically rigorous, this book can be appealing to graduate students in Mathematics or Physics seeking specialization in general relativity, geometry or partial differential equations. Prerequisites include proficiency in differential geometry and the basic principles of relativity. Readers who are familiar with special relativity and have taken a course either in Riemannian geometry (for students of Mathematics) or in general relativity (for those in Physics) can benefit from this book.

The book begins with a brief review of supersymmetry and the construction of the minimal supersymmetric standard model and approaches to supersymmetry breaking. General non-perturbative methods are also reviewing leading to the development of holomorphy and the Affleck-Dine-Seiberg superpotential as powerful tools for analyzing supersymmetric theories. Seiberg duality is discussed in detail, with many example applications provided, with special attention paid to its use in understanding dynamical supersymmetry breaking. The Seiberg-Witten theory of monopoles is introduced through the analysis of simpler N=1 analogues. Superconformal field theories are described along with the most recent development known as "a-maximization." Supergravity theories are examined in 4, 10, and 11 dimensions, allowing for a discussion of anomaly and gaugino mediation, and setting the stage for the anti-de-Sitter/conformal field theory correspondence. This book is unique in containing an overview of the important developments in supersymmetry since the publication of "Supersymmetry and Supergravity" by Wess and Bagger. It also strives to cover topics that are of interest to both formal and phenomenological theorists.

This book is a pedagogical guide on how to make computations in direct dark matter (DM) detection. The theory behind the calculation of direct detection cross sections and rates is presented, touching aspects related to elementary particle physics, hadronic physics, nuclear physics, and astrophysics. The book is structured in self-contained sections, covering several topics ranging from the scattering kinematics to the phenomenology of direct DM searches. It follows a model-independent approach, aiming at providing the readers with all that is needed to understand the theory and start their own analysis. Meant for graduate students and researchers with interests in particle physics and phenomenology, it is enriched with several worked examples from standard and non-standard particle DM models. Senior researchers working in different areas related to dark matter, like particle and nuclear physics, astrophysics, and cosmology, find in this book a useful and updated guide for reference.

This textbook introduces the special theory of relativity at a level which is accessible to undergraduate students and even high school students with a strong foundation in algebra. The presentation emphasizes clean algebraic and geometrical methods, visualized with plenty of illustrations, resulting in a textbook that is modern and serious yet accessible. Replete with many solved exercises and copious spacetime diagrams, this book will help students develop relativistic intuition when encountering the subject for the first time. The emphasis on geometric methods, combined with the pedagogically appealing k-calculus approach, makes this book ideal for a self-contained course on special relativity or as supplementary reading for modern physics courses. It will also appeal to high schoolers with a strong math background who want to get ahead.

This textbook introduces the topic of special relativity, with a particular emphasis upon light-matter interaction and the production of light in plasma. The physics of special relativity is intuitively developed and related to the radiative processes of light. The book reviews the underlying theory of special relativity, before extending the discussion to applications frequently encountered by postgraduates and researchers in astrophysics, high power laser interactions and the users of specialized light sources, such as synchrotrons and free electron lasers. A highly pedagogical approach is adopted throughout, and numerous exercises are included within each chapter to reinforce the presentation of key concepts and applications of the material.

This book recounts the developments of fundamental electrodynamics from Ampère's investigation of the forces between electric currents to Einstein's introduction of a new doctrine of space and time. The emphasis is on the diverse, evolving practices of electrodynamics and the interactions between the corresponding scientific traditions. A richly documented, clearly written, and abundantly illustrated history of the subject.

Professor Chandrasekhar's work is an attempt by a distinguished practising scientist to read and comprehend the enormous intellectual achievement of the Principia without recourse to secondary sources. This text has stimulated great interest and debate among the scientific community, illuminating the brilliance of Newton's work under the gaze of Chandrasekhar's rare perception.

A host of astrophysical measurements suggest that most of the matter in the Universe is an invisible, nonluminous substance that physicists call "dark matter." Understanding the nature of dark matter is one of the greatest challenges of modern physics and is of paramount importance to our theories of cosmology and particle physics. This text explores one of the leading hypotheses to explain dark matter: that it consists of ultralight bosons forming an oscillating field that feebly interacts with light and matter. Many new experiments have emerged over the last decade to test this hypothesis, involving state-of-the-art microwave cavities, precision nuclear magnetic resonance (NMR) measurements, dark matter "radios," and synchronized global networks of atomic clocks, magnetometers, and interferometers. The editors have gathered leading experts from around the world to present the theories motivating these searches, evidence about dark matter from astrophysics, and the diverse experimental techniques employed in searches for ultralight bosonic dark matter. The text provides a comprehensive and accessible introduction to this blossoming field of research for advanced undergraduates, beginning graduate students, or anyone new to the field, with tutorials and solved problems in every chapter. The multifaceted nature of the research - combining ideas and methods from atomic, molecular, and optical physics, nuclear physics, condensed matter physics, electrical engineering, particle physics, astrophysics, and cosmology - makes this introductory approach attractive for beginning researchers as well as members of the broader scientific community. This is an open access book.

Many people know that Einstein invented the theory of relativity, but only few have more than a superficial idea of its content. This book aims to explain the basic features of relativity in detail, emphasising the geometrical aspects by using a large number of diagrams, and assuming no knowledge of higher level mathematics.

Starting out from humankind's earliest ideas about the cosmos, this book gives the reader a clear overview of our current understanding of the universe, including big bang theories and the formation of stars and galaxies, as well as addressing open questions. The author shows how our present view gradually developed from observations, and also how the outcome of ongoing research may still change this view. The book brings together concepts in physics and astronomy, including some history in both cases. The text is descriptive rather than technical: the goal is to present things rigorously and without oversimplification, by highlighting the crucial physical concepts. The only prerequisite is a qualitative knowledge of basic physics concepts at high-school level.

This book is about supergravity, which combines the principles of general relativity and local gauge invariance with the idea of supersymmetries between bosonic and fermionic degrees of freedom. The authors give a thorough and pedagogical introduction to the subject suitable for beginning graduate or advanced undergraduate students in theoretical high energy physics or mathematical physics. Interested researchers working in these or related areas are also addressed. The level of the presentation assumes a working knowledge of general relativity and basic notions of differential geometry as well as some familiarity with global supersymmetry in relativistic field theories. Bypassing curved superspace and other more technical approaches, the book starts from the simple idea of supersymmetry as a local gauge symmetry and derives the mathematical and physical properties of supergravity in a direct and "minimalistic" way, using a combination of explicit computations and geometrical reasoning. Key topics include spinors in curved spacetime, pure supergravity with and without a cosmological constant, matter couplings in global and local supersymmetry, phenomenological and cosmological implications, extended supergravity, gauged supergravity and supergravity in higher spacetime dimensions.

Offers an accessible text and reference (a cosmic-ray manual) for graduate students entering the field and high-energy astrophysicists will find this an accessible cosmic-ray manual Easy to read for the general astronomer, the first part describes the standard model of cosmic rays based on our understanding of modern particle physics. Presents the acceleration scenario in some detail in supernovae explosions as well as in the passage of cosmic rays through the Galaxy. Compares experimental data in the atmosphere as well as underground are compared with theoretical models

Clarity, readability, and rigor combine in the third edition of this widely used textbook to provide the first step into general relativity for advanced undergraduates with a minimal background in mathematics. Topics within relativity that fascinate astrophysics researchers and students alike are covered with Schutz's characteristic ease and authority, from black holes to relativistic objects, from pulsars to the study of the Universe as a whole. This third edition contains discoveries by astronomers that require general relativity for their explanation; two chapters on gravitational waves, including direct detections of gravitational waves and their observations' impact on cosmological measurements; new information on black holes and neutron stars; and greater insight into the expansion of the Universe. Over 300 exercises, many new to this edition, give students the confidence to work with general relativity and the necessary mathematics, while the informal writing style and worked examples make the subject matter easily accessible.

Black Holes are regions of space-time where the gravitational field is so strong that not even light can escape. There has been much written on black holes, however in most cases they are treated as isolated objects. The author has found a number of cases in which the interaction of a black hole with another strong-field system (such as the background universe or another black hole) could be treated analytically. This includes using the powerful method of matched asymptotic expansions. In this book the author considers these wider ranging problems and examples for the first time. This book will be widely read by all those working in gravitation, and PhD students in mathematical physics.

Providing a comprehensive exposition of the transactional interpretation (TI) of quantum mechanics, this book sheds new light on long-standing problems in quantum theory such as the physical meaning of the 'Born Rule' for the probabilities of measurement results, and demonstrates the ability of TI to solve the measurement problem of quantum mechanics. It provides robust refutations of various objections and challenges to TI, such as Maudlin's inconsistency challenge, and explicitly extends TI into the relativistic domain, providing new insight into the basic compatibility of TI with relativity and the meaning of 'virtual particles.' It breaks new ground in approaches to interpreting quantum theory and presents a compelling new ontological picture of quantum reality. This substantially revised and updated second edition is ideal for researchers and graduate students interested in the philosophy of physics and the interpretation of quantum mechanics.

This thorough introduction to Einstein's special theory of relativity is suitable for anyone with a minimum of one year of undergraduate physics with calculus. The authors cover every aspect of special relativity, including the impact of special relativity in quantum theory, with an introduction to relativistic quantum mechanics and quantum field theory. They also discuss the group theory of the Lorentz group, supersymmetry, and such cutting-edge topics as general relativity, the standard model of elementary particles and its extensions, and superstring theory, giving a survey of important unsolved problems. The book is accompanied by an interactive CD-ROM illustrating classic problems in relativity involving motion.

Based on lectures given at a summer school on computer algebra, the book provides a didactic description of the facilities available in three computor algebra systems - MAPLE, REDUCE and SHEEP - for performing calculations in the algebra-intensive field of general relativity. With MAPLE and REDUCE, two widespread great-purpose systems, the reader is shown how to use currently available packages to perform calculations with respect to tetrads, co-ordinate systems, and Poincare` gauge theory. The section on SHEEP and Stensor, being the first published book on these systems, explains how to use these systems to tackle a wide range of calculations with respect to tackle a wide range of calculations in general relativity, including the manipulation of indicial formulae. For the researcher in general relativity, the book therefore promises a wide overview of the facilities available in computer algebra to lessen the burden of the lengthy, error-prone calculations involved in their research.

This book presents Special Relativity in a language accessible to students while avoiding the burdens of geometry, tensor calculus, space-time symmetries, and the introduction of four vectors. The search for clarity in the fundamental questions about Relativity, the discussion of historical developments before and after 1905, the strong connection to current research topics, many solved examples and problems, and illustrations of the material in colloquial discussions are the most significant and original assets of this book. Importantly for first-time students, Special Relativity is presented such that nothing needs to be called paradoxical or apparent; everything is explained. The content of this volume develops and builds on the book Relativity Matters (Springer, 2017). However, this presentation of Special Relativity does not require 4-vector tools. The relevant material has been extended and reformulated, with additional examples and clarifications. This introduction of Special Relativity offers conceptual insights reaching well beyond the usual method of teaching relativity. It considers relevant developments after the discovery of General Relativity (which itself is not presented), and advances the reader into contemporary research fields. This presentation of Special Relativity is connected to present day research topics in particle, nuclear, and high intensity pulsed laser physics and is complemented by the current cosmological perspective. The conceptual reach of Special Relativity today extends significantly further compared even to a few decades ago. As the book progresses, the qualitative and historical introduction turns into a textbook-style presentation with many detailed results derived in an explicit manner. The reader reaching the end of this text needs knowledge of classical mechanics, a good command of elementary algebra, basic knowledge of calculus, and introductory know-how of electromagnetism.

This compact yet informative Guide presents an accessible route through Special Relativity, taking a modern axiomatic and geometrical approach. It begins by explaining key concepts and introducing Einstein's postulates. The consequences of the postulates - length contraction and time dilation - are unravelled qualitatively and then quantitatively. These strands are then tied together using the mathematical framework of the Lorentz transformation, before applying these ideas to kinematics and dynamics. This volume demonstrates the essential simplicity of the core ideas of Special Relativity, while acknowledging the challenges of developing new intuitions and dealing with the apparent paradoxes that arise. A valuable supplementary resource for intermediate undergraduates, as well as independent learners with some technical background, the Guide includes numerous exercises with hints and notes provided online. It lays the foundations for further study in General Relativity, which is introduced briefly in an appendix.

In the late 20th and beginning 21st century high-precision astronomy, positioning and metrology strongly rely on general relativity. Supported by exercises and solutions this book offers graduate students and researchers entering those fields a self-contained and exhaustive but accessible treatment of applied general relativity. The book is written in a homogenous (graduate level textbook) style allowing the reader to understand the arguments step by step. It first introduces the mathematical and theoretical foundations of gravity theory and then concentrates on its general relativistic applications: clock rates, clock sychronization, establishment of time scales, astronomical references frames, relativistic astrometry, celestial mechanics and metrology. The authors present up-to-date relativistic models for applied techniques such as Satellite LASER Ranging (SLR), Lunar LASER Ranging (LLR), Globale Navigation Satellite Systems (GNSS), Very Large Baseline Interferometry (VLBI), radar measurements, gyroscopes and pulsar timing. A list of acronyms helps the reader keep an overview and a mathematical appendix provides required functions and terms.

Einstein's theories of special relativity and general relativity form a core part of today's undergraduate (or Masters-level) physics curriculum. This is a supplementary problem book or student's manual, consisting of 150 problems in each of special and general relativity. The problems, which have been developed, tested and refined by the authors over the past two decades, are a mixture of short-form and multi-part extended problems, with hints provided where appropriate. Complete solutions are elaborated for every problem, in a different section of the book; some solutions include brief discussions on their physical or historical significance. Designed as a companion text to complement a main relativity textbook, it does not assume access to any specific textbook. This is a helpful resource for advanced students, for self-study, a source of problems for university teaching assistants, or as inspiration for instructors and examiners constructing problems for their lectures, homework or exams.

Einstein's theories of special relativity and general relativity form a core part of today's undergraduate (or Masters-level) physics curriculum. This is a supplementary problem book or student's manual, consisting of 150 problems in each of special and general relativity. The problems, which have been developed, tested and refined by the authors over the past two decades, are a mixture of short-form and multi-part extended problems, with hints provided where appropriate. Complete solutions are elaborated for every problem, in a different section of the book; some solutions include brief discussions on their physical or historical significance. Designed as a companion text to complement a main relativity textbook, it does not assume access to any specific textbook. This is a helpful resource for advanced students, for self-study, a source of problems for university teaching assistants, or as inspiration for instructors and examiners constructing problems for their lectures, homework or exams.

The problem of quantum gravity is often viewed as the most pressing unresolved problem of modern physics: our theories of spacetime and matter, described respectively by general relativity (Einstein's theory of gravitation and spacetime) and quantum mechanics (our best theory of matter and the other forces of nature) resist unification. Covered with Deep Mist provides the first book-length treatment of the history of quantum gravity, focusing on its origins and earliest stages of development until the mid-1950s. Readers will be guided through the impacts on the problem of quantum gravity resulting from changes in the two ingredient theories, quantum theory and general relativity, which were themselves still under construction in the years studied. We examine how several of the core approaches of today were formed in an era when the field was highly unfashionable. The book aims to be accessible to a broad range of readers and goes beyond a merely technical examination to include social and cultural factors involved in the changing fortunes of the field. Suitable for both newcomers and seasoned quantum gravity professionals, the book will shine new light on this century-old, unresolved problem.