This book is an introduction to the theory of supersymmetry, which is a cornerstone to understanding the physics of elementary particles beyond the so-called "Standard Model". Supersymmetry is the first introductory book on this modern and increasingly popular subject.

Ernst Mach (1838-1916) zahlt zu den bedeutendsten Naturwissenschaftlern und Philosophen des 19. und 20. Jahrhunderts. In der Physik gilt er als Wegbereiter von Einsteins Relativitatstheorie und Kontrahent von Boltzmanns Atomistik. In der Biologie, Psychologie und Physiologie wird er als Pionier einer empiristischen und gestalthaften "Analyse der Empfindungen" betrachtet. In der Wissenschaftsphilosophie schliesslich war er Vorbild des Wiener Kreises mit dem Verein Ernst Mach und Wegbereiter einer integrierten Wissenschaftsgeschichte und Wissenschaftstheorie. Der Band versammelt die deutschsprachigen Beitrage zum Symposium anlasslich des 100. Todestages von Ernst Mach. Im Mittelpunkt der internationalen Konferenz im Juni 2016 an der Universitat Wien und der OEsterreichischen Akademie der Wissenschaften standen Leben, Werk und Wirkung des Naturforschers und Philosophen. Der Band bietet eine kritische Bestandsaufnahme von Machs Lebenswerk vor dem Hintergrund der aktuellen Forschung und Historiografie. Die Autoren untersuchen unter anderem * seine Bedeutung fur die Herausbildung einer naturwissenschaftlichen Psychologie * Machs historisch-kritische Methode * die Rolle der Kinematographie * die Rezeption durch Aleksander Bogdanov * das Verhaltnis zu Sigmund Freuds Psychoanalyse Der Band erscheint in der Reihe "Veroeffentlichungen des Instituts Wiener Kreis" und richtet sich an Forschende auf den Gebieten der Wissenschaftsphilosophie, -geschichte und -theorie sowie der Kulturwissenschaften und der Wahrnehmungspsychologie.

This book introduces the phenomenology of gravitational lensing in an accessible manner and provides a thorough discussion of the related astrophysical applications. It is intended for advanced undergraduates and graduate students who want to start working in this rapidly evolving field. This includes also senior researchers who are interested in ongoing or future surveys and missions such as DES, Euclid, WFIRST, LSST. The reader is guided through many fascinating topics related to gravitational lensing like the structure of our galaxy, the searching for exoplanets, the investigation of dark matter in galaxies and galaxy clusters, and several aspects of cosmology, including dark energy and the cosmic microwave background. The author, who has gained valuable experience as academic teacher, guides the readers towards the comprehension of the theory of gravitational lensing and related observational techniques by using simple codes written in python. This approach, beyond facilitating the understanding of gravitational lensing, is preparatory for learning the python programming language which is gaining large popularity both in academia and in the private sector.

Professor Sir Roger Penrose's work, spanning fifty years of science, with over five thousand pages and more than three hundred papers, has been collected together for the first time and arranged chronologically over six volumes, each with an introduction from the author. Where relevant, individual papers also come with specific introductions or notes. Many important realizations concerning twistor theory occurred during the short period of this third volume, providing a new perspective on the way that mathematical features of the complex geometry of twistor theory relate to actual physical fields. Following on from the nonlinear graviton construction, a twistor construction was found for (anti-)self-dual electromagnetism allowing the general (anti-)self-dual Yang-Mills field to be obtained. It became clear that some features of twistor contour integrals could be understood in terms of holomorphic sheaf cohomology. During this period, the Oxford research group founded the informal publication, Twistor Newsletter. This volume also contains the influential Weyl curvature hypothesis and new forms of Penrose tiles.

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.

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 brief approaches General Relativity from a planetary navigation perspective, delving into the unconventional mathematical methods required to produce computer software for space missions. It provides a derivation of the Einstein field equations and describes experiments performed on the Near Earth Asteroid Rendezvous mission, spanning General Relativity Theory from the fundamental assumptions to experimental verification. The software used for planetary missions is derived from mathematics that use matrix notation. An alternative is to use Einstein summation notation, which enables the mathematics to be presented in a compact form but makes the geometry difficult to understand. In this book, the relationship of matrix notation to summation notation is shown. The purpose is to enable the reader to derive the mathematics used in the software in either matrix notation or summation notation. This brief is a useful tool for advanced students and young professionals embarking on careers in planetary navigation.

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.

Einstein's general theory of relativity can be a notoriously difficult subject for students approaching it for the first time, with arcane mathematical concepts such as connection coefficients and tensors adorned with a forest of indices. This book is an elementary introduction to Einstein's theory and the physics of curved space-times that avoids these complications as much as possible. Its first half describes the physics of black holes, gravitational waves and the expanding Universe, without using tensors. Only in the second half are Einstein's field equations derived and used to explain the dynamical evolution of the early Universe and the creation of the first elements. Each chapter concludes with problem sets and technical mathematical details are given in the appendices. This short text is intended for undergraduate physics students who have taken courses in special relativity and advanced mechanics.

This book presents a review of various issues related to Lorentz symmetry breaking. Explicitly, we consider (i) motivations for introducing Lorentz symmetry breaking, (ii) classical aspects of Lorentz-breaking field theory models including typical forms of Lorentz-breaking additive terms, wave propagation in Lorentz-breaking theories, and mechanisms for breaking the Lorentz symmetry; (iii) quantum corrections in Lorentz-breaking theories, especially the possibilities for perturbation generating the most interesting Lorentz-breaking terms; (iv) correspondence between non-commutative field theories and Lorentz symmetry breaking; (v) supersymmetric Lorentz-breaking theories; and (vi) Lorentz symmetry breaking in a curved space-time. We close the book with the review of experimental studies of Lorentz symmetry breaking. The importance and relevance of these topics are explained, first, by studies of limits of applicability of the Lorentz symmetry, second, by searches of the possible extensions of the standard model, including the Lorentz-breaking ones, and need to study their properties, third, by the relation between Lorentz symmetry breaking with string theory, fourth, by the problem of formulating a consistent quantum gravity theory, so that various modified gravity models are to be examined.

DROPOUT. PACIFIST. PHYSICIST. CASANOVA. REFUGEE. REBEL. GENIUS. THINK YOU KNOW EINSTEIN? THINK AGAIN His face is instantly recognisable. His name is shorthand for genius. Today, he's a figurehead as much as a man, symbolic of things larger than himself: of scientific progress, of the human mind, even of the age. But who was Einstein really? The Nobel Prize-winning physicist who discovered relativity, black holes and E = mc2, dined with Charlie Chaplin in Hollywood and was the inspiration for (highly radioactive) element 99, Albert Einstein was also a high school dropout with an FBI file 1,400 pages long. In this book, Samuel Graydon brings history's most famous scientist back to life. From his lost daughter to escaping the Nazis, from his love letters to unlikely inventions, from telling jokes to cheer up his sad parrot Bibo to refusing the Presidency of Israel, through the discoveries and thought experiments that changed science, Einstein in Time and Space tells 99 unforgettable stories of the man who redefined how we view our universe and our place within it.

Rather than focusing on the contributions of theoretical physicists to the understanding of the subatomic world and of the beginning of the universe - as most popular science books on particle physics do - this book is different in that, firstly, the main focus is on machine inventors and builders and, secondly, particle accelerators are not only described as discovery tools but also for their contributions to tumour diagnosis and therapy. The characters of well-known (e.g. Ernest Lawrence) and mostly unknown actors (e.g. Nicholas Christofilos) are outlined, including many colourful quotations. The overall picture supports the author's motto: "Physics is beautiful and useful". Advance appraisal: "Accelerators go all the way from the unique and gargantuan Large Hadron Collider to thousands of smaller versions in hospitals and industry. Ugo Amaldi has experience across the range. He has worked at CERN and has for many years been driving the application of accelerators in medicine. This is a must-read introduction to this frontier of modern technology, written beautifully by a world expert." Frank Close, Professor of Physics at Oxford University author of "The Infinity Puzzle" "This book should be read by school teachers and all those interested in the exploration of the microcosm and its relation to cosmology, and in the use of accelerators for medical applications. With a light hand and without formulae the autho r easily explains complicated matters, spicing up the text with amusing historical anecdotes. His reputation as an outstanding scientist in all the fields treated guarantees high standards." Herwig Schopper, former CERN Director General author of "LEP - The Lord of the Collider Rings at CERN" "This book tells the story of modern physics with an unusual emphasis on the machine-builders who made it all possible, and their machines. Learning to accelerate particles has enabled physicists to probe the subatomic world and gain a deeper understanding of the cosmos. It has also brought numerous benefits to medicine, from the primitive X-ray machines of over a century ago to today's developments in hadron therapy for cancer. Amaldi tells this story in a most fascinating way." Edward Witten, Professor of Mathematical Physics at the Institute for Advanced Study in Princeton; Fields Medal (1990)

With a focus on modified gravity this book presents a review of the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research. General Relativity and the CDM framework are currently the standard lore and constitute the concordance paradigm of cosmology. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology in the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. In this review all extended theories and scenarios are first examined under the light of theoretical consistency, and are then applied in various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology has been able to offer in the last two decades. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature, allowing readers to get a clear overview of the state of the art and where the field of modified gravity is likely to go. This work was performed in the framework of the COST European Action "Cosmology and Astrophysics Network for Theoretical Advances and Training Actions" - CANTATA.

This thesis is devoted to the systematic study of non-local theories that respect Lorentz invariance and are devoid of new, unphysical degrees of freedom. Such theories are attractive for phenomenological applications since they are mostly unconstrained by current experiments. Non-locality has played an increasingly important role in the physics of the last decades, appearing in effective actions in quantum field theory, and arising naturally in string theory and non-commutative geometry. It may even be a necessary ingredient for quantum theories of gravity. It is a feature of quantum entanglement, and may even solve the long-standing black hole information loss problem. "Non-locality" is a broad concept with many promising and fruitful applications in theoretical and mathematical physics. After a historical and pedagogical introduction into the concept of non-locality the author develops the notion of non-local Green functions to study various non-local weak-field problems in quantum mechanics, quantum field theory, gravity, and quantum field theory in curved spacetime. This thesis fills a gap in the literature by providing a self-contained exploration of weak-field effects in non-local theories, thereby establishing a "non-local intuition" which may serve as a stepping stone for studies of the full, non-linear problem of non-locality.

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.

Owing to the increased accuracy requirements in fields such as astrometry and geodesy the general theory of relativity must be taken into account for any mission requiring highly accurate orbit information and for practically all observation and measurement techniques. This book highlights the confluence of Applied Mathematics, Physics and Space Science as seen from Einstein's general theory of relativity and aims to bridge the gap between theoretical and applied domains. The book investigates three distinct areas of general relativity: Exact solutions of the Einstein field equations of gravitation. Dynamics of near-Earth objects and solar system bodies. Relativistic orbitography. This book is an updated and expanded version of the author's PhD thesis which was awarded the International Astronomical Union PhD prize in Division A: Fundamental Astronomy. Included is a new introduction aimed at graduate students of General Relativity and extended discussions and results on topics in post-Newtonian dynamics and general relativistic spacecraft propagation.

The book is about exact space-time models of the gravitational fields produced by gravitational radiation. The authors' extensive work in the field is reviewed in order to stimulate the study of such models, that have been known for a long time, and to highlight interesting physical aspects of the existing models in some novel detail. There is an underlying simplicity to the gravitational radiation studied in this book. Apart from the basic assumption that the radiation has clearly identifiable wave fronts, the gravitational waves studied are directly analogous to electromagnetic waves. The book is meant for advanced students and researchers who have a knowledge of general relativity sufficient to carry out research in the field.

The ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realising this goal by introducing geometric descriptions of systems such as quantum gravity, fermionic particles and the origins of the Universe itself. The author extends the applicability of previous work by Vilkovisky, DeWitt and others to include theories with spin 1/2 and spin 2 degrees of freedom. In addition, he introduces a geometric description of the potential term in a quantum field theory through a process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation, where they show how geometry can help answer a long-standing question about the initial conditions of the Universe. This publication is aimed at graduate and advanced undergraduate students and provides a pedagogical introduction to the exciting topic of field space covariance and the complete geometrization of quantum field theory.

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.

Newton's Philosophiae Naturalis Principia Mathematica provides a coherent and deductive presentation of his discovery of the universal law of gravity. The Principia is, in fact, a model for all mathematical physics.

Representing a decade's work from one of the world's most distinguished physicists, this major publication is, as far as is known, the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breathtaking economy of Newton's methods. Chandrasehkar's work is an attempt by a distinguished practising scientist to read and comprehend the enormous intellectual achievement of the Principia. This book will stimulate great interest and debate among the scientific community, illuminating the brilliance of Newton's work under the steady gaze of Chandrasekhar's rare perception.

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.

These three lectures cover a certain aspect of complexity and black holes, namely the relation to the second law of thermodynamics. The first lecture describes the meaning of quantum complexity, the analogy between entropy and complexity, and the second law of complexity. Lecture two reviews the connection between the second law of complexity and the interior of black holes. Prof. L. Susskind discusses how firewalls are related to periods of non-increasing complexity which typically only occur after an exponentially long time. The final lecture is about the thermodynamics of complexity, and "uncomplexity" as a resource for doing computational work. The author explains the remarkable power of "one clean qubit," in both computational terms and in space-time terms. This book is intended for graduate students and researchers who want to take the first steps towards the mysteries of black holes and their complexity.