Following the birth of the laser in 1960, the field of "nonlinear optics" rapidly emerged.

Today, laser intensities and pulse durations are readily available, for which the concepts and approximations of traditional nonlinear optics no longer apply. In this regime of "extreme nonlinear optics," a large variety of novel and unusual effects arise, for example frequency doubling in inversion symmetric materials or high-harmonic generation in gases, which can lead to attosecond electromagnetic pulses or pulse trains. Other examples of "extreme nonlinear optics" cover diverse areas such as solid-state physics, atomic physics, relativistic free electrons in a vacuum and even the vacuum itself.

This book starts with an introduction to the field based primarily on extensions of two famous textbook examples, namely the Lorentz oscillator model and the Drude model. Here the level of sophistication should be accessible to any undergraduate physics student. Many graphical illustrations and examples are given. The following chapters gradually guide the student towards the current "state of the art" and provide a comprehensive overview of the field. Every chapter is accompanied by exercises to deepen the reader's understanding of important topics, with detailed solutions at the end of the book.

This books aims at giving an overview over theoretical and phenomenological aspects of particle astrophysics and particle cosmology. To be of interest for both students and researchers in neighboring fields of physics, it keeps a balance between well established foundations that will not significantly change in the future and a more in-depth treatment of selected subfields in which significant new developments have been taking place recently. These include high energy particle astrophysics, such as cosmic high energy neutrinos, the interplay between detection techniques of dark matter in the laboratory and in high energy cosmic radiation, axion-like particles, and relics of the early Universe such as primordial magnetic fields and gravitational waves. It also contains exercises and thus will be suitable for both introductory and advanced courses in astroparticle physics.

This work investigates gravitational wave production in the early universe and identifies potentially observable features, thereby paving the way for future gravitational wave experiments. It focuses on gravitational wave production in two scenarios: inflation in a model inspired by loop quantum gravity, and preheating at the end of inflation. In the first part, it is demonstrated that gravitational waves' spectrum differs from the result obtained using ordinary general relativity, with potentially observable consequences that could yield insights into quantum gravity. In the second part, it is shown that the cosmic gravitational wave background is anisotropic at a level that could be detected by future experiments. Gravitational waves promise to be an rich source of information on the early universe. To them, the universe has been transparent from its earliest moments, so they can give us an unobstructed view of the Big Bang and a means to probe the fundamental laws of nature at very high energies.

This thesis reports the measurement of muon neutrino and antineutrino disappearance and electron neutrino and antineutrino appearance in a muon neutrino and antineutrino beam using the T2K experiment. It describes a result in neutrino physics that is a pioneering indication of charge-parity (CP) violation in neutrino oscillation; the first to be obtained from a single experiment. Neutrinos are some of the most abundant-but elusive-particles in the universe, and may provide a promising place to look for a potential solution to the puzzle of matter/antimatter imbalance in the observable universe. It has been firmly established that neutrinos can change flavour (or 'oscillate'), as recognised by the 2015 Nobel Prize. The theory of neutrino oscillation allows for neutrinos and antineutrinos to oscillate differently (CP violation), and may provide insights into why our universe is matter-dominated. Bayesian statistical methods, including the Markov Chain Monte Carlo fitting technique, are used to simultaneously optimise several hundred systematic parameters describing detector, beam, and neutrino interaction uncertainties as well as the six oscillation parameters.

This thesis describes one of the most precise experimental tests of Lorentz symmetry in electrodynamics by light-speed anisotropy measurement with an asymmetric optical ring cavity. The author aims to answer the fundamental, hypothetical debate on Lorentz symmetry in the Universe. He concludes that the symmetry is protected within an error of 10-15, which means providing one of the most stringent upper limits on the violation of the Lorentz symmetry in the framework of the Standard Model Extension. It introduces the following three keys which play an important role in achieving high-precision measurement: (1) a high-index element (silicon) interpolated into part of the light paths in the optical ring cavity, which improves sensitivity to the violation of the Lorentz symmetry, (2) double-pass configuration of the interferometer, which suppresses environmental noises, and (3) continuous data acquisition by rotating the optical ring cavity, which makes it possible to search for higher-order violations of Lorentz symmetry. In addition to those well-described keys, a comprehensive summary from theoretical formulations to experimental design details, data acquisition, and data analysis helps the reader follow up the experiments precisely.

Physicists are pondering on the possibility of simulating black holes in the laboratory by means of various "analog models". These analog models, typically based on condensed matter physics, can be used to help us understand general relativity (Einstein's gravity); conversely, abstract techniques developed in general relativity can sometimes be used to help us understand certain aspects of condensed matter physics. This book contains 13 chapters - written by experts in general relativity, particle physics, and condensed matter physics - that explore various aspects of this two-way traffic.

This thesis describes in detail a search for weakly interacting massive particles as possible dark matter candidates, making use of so-called mono-jet events. It includes a detailed description of the run-1 system, important operational challenges, and the upgrade for run-2. The nature of dark matter, which accounts for roughly 25% of the energy-matter content of the universe, is one of the biggest open questions in fundamental science. The analysis is based on the full set of proton-proton collisions collected by the ATLAS experiment at the Large Hadron Collider at s = 8 TeV. Special attention is given to the experimental challenges and analysis techniques, as well as the overall scientific context beyond particle physics. The results complement those of non-collider experiments and yield some of the strongest exclusion bounds on parameters of dark matter models by the end of the Large Hadron Collider run-1. Details of the upgrade of the ATLAS Central Trigger for run-2 are also included.

Written by international experts, this book explores the possibilities for the next 20 years in conducting gravitational experiments in space that would make the most of the new and much-improved existing capabilities. They start from the premise that over the next decade the gravitational physics community will benefit from dramatic improvements in many technologies critical to the tests of gravity. This volume contains a comprehensive presentation of the theory, technology, missions and projects on relativistic gravity in space.

The 16th conference of the International Society on General Relativity and Gravitation (GR16), held at the International Convention Centre in Durban, South Africa, from 15 to 21 July, was attended by 450 delegates from around the world. The scientific programme comprised 18 plenary lectures, I public lecture and 19 workshops which, excepting 3 plenary lectures, are presented in this proceedings. It was the first major international conference on general relativity and gravitation held on the African continent.

The year 1995 marks the 90th anniversary of Einstein's first description of the theory of relativity. In this unique reference book, Einstein's multi-disciplinary contributions to science and society are presented in an easy-to-read dictionary format. The book is a synthesis of existing literature on Einstein including his own writings, biographies, and the secondary literature published during the past 40 years. The author presents all facets of Einstein's life, which began in Ulm, Germany, and came to an end in Princeton, New Jersey, spanning a tumultuous period marked by two world wars and the dawn of the atomic age. The year 1995 marks the 90th anniversary of Einstein's first description of the theory of relativity. In this unique reference book, Einstein's multi-disciplinary contributions to science and society are presented in an easy-to-read dictionary format. Einstein's personal life, physics, philosophy, and politics are covered in more than 600 entries. The book is a synthesis of existing literature on Einstein, including his own writings, biographies, and the secondary literature published during the past 40 years. The author presents all facets of Einstein's life, which began in Ulm, Germany, and came to an end in Princeton, New Jersey, spanning a tumultuous period marked by two world wars and the dawn of the atomic age. Abundant information is presented in a style that is accessible to students and non-scientists. Entries are cross-referenced for easy access to related information. The work also includes a chronological synopsis, a genealogical chart, and several appendices.

The Nordic mythological Cosmic Serpent, Ouroboros, is said to be coiled in the depths of the sea, surrounding the Earth with its tail in its mouth. In physics, this snake is a metaphor for the Universe, where the head, symbolizing the largest entity the Cosmos is one with the tail, symbolizing the smallest the fundamental particle.

Particle accelerators, colliders and detectors are built by physicists and engineers to uncover the nature of the Universe while discovering its building blocks. Charming the Cosmic Snake takes the readers through the science behind these experimental machines: the physics principles that each stage of the development of particle accelerators helped to reveal, and the particles they helped to discover. The book culminates with a description of the Large Hadron Collider, one of the world s largest and most complex machines operating in a 27-km circumference tunnel near Geneva. That collider may prove or disprove many of our basic theories about the nature of matter.

The book provides the material honestly without misrepresenting the science for the sake of excitement or glossing over difficult notions. The principles behind each type of accelerator is made accessible to the undergraduate student and even to a lay reader with cartoons, illustrations and metaphors. Simultaneously, the book also caters to different levels of reader s background and provides additional materials for the more interested or diligent reader.

The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation.

In this XVII Course of the International School of Cosmology and Gravitation devoted to "ADVANCES IN THE INTERPLAY BETWEEN QUANTUM AND GRAVITY PHYSICS" we have considered different aspects of the influence of gravity on quantum systems. In order to achieve this aim, in many lectures, seminars and discussions we have strengthened the interplay between gravity and quantum systems starting from the situation in the early universe based on astrophysical observations, up to the earthly based experiments with atom interferometry for probing the structure of space-time. Thus we have had timely lectures on the quantum field and horizon of a black hole including reviews of the problem of black holes thermodynamics and entropy, quantum information, quantum black holes, quantum evaporation and Hawking radiation, recent advances in stockastic gravity. We have also discussed quantum fluctuations in inflationary universe, quantum effects and reheating after inflation, and superplanckian energies in Hawking radiation. In this regard the subject of spinors in purely affine space-time and Dirac matter according to Weyl in the generalized theory of gravitation were developed . The dualism between space-time and matter has been deeply analyzed in order to see why, for general relativity, this is an obstacle for quantization of the theory. Also canonical Gravity and Mach's principle, torsion and curvature as commutator for Quantum Gravity and Dirac Geometry of real space-time were analysed, together with the problem of 5-Dimensional Projective Unified Field theory and Multidimensional Gravity and Cosmology.

The current volume of the Parmenides Series "On Thinking" addresses our deepest and most personal experience of the world, the experience of "the present," from a modern perspective combining physics and philosophy. Many prominent researchers have contributed articles to the volume, in which they present models and express their opinions on and, in some cases, also their skepticism about the subject and how it may be (or may not be) addressed, as well as which aspects they consider most relevant in this context. While Einstein might have once hoped that "the present" would find its place in the theory of general relativity, in a later discussion with Carnap he expressed his disappointment that he was never able to achieve this goal. This collection of articles provides a unique overview of different modern approaches, representing not only a valuable summary for experts, but also a nearly inexhaustible source of profound and novel ideas for those who are simply interested in this question.

This volume from the Einstein Studies Series is based largely on papers presented at the Sixth International Conference on the History of General Relativity, held in Amsterdam on June 26-29, 2002. These contributions from notable experts offer both new and historical insights on gravitation, general relativity, cosmology, unified field theory, and the history of science.

Topics discussed include the prehistory of special relativity, early attempts at a relativistic theory of gravitation, the beginnings of general relativity, the problem of motion in the context of relativity, conservation laws, the axiomatization of relativity, classical and contemporary cosmology, gravitation and electromagnetism, quantum gravity, and relativity as seen through the eyes of the public and renowned relativists.

Contributors: K. Brading; G. Gale; H.F.M. Goenner; J. Goldberg; S. Katzir; D. Kennefick; H. Kragh; C. Lehner; U. Majer; J. Mattingly; E.T. Newman; J.D. Norton; J. Renn; R. Rynasiewicz; J.M. SAnchez-Ron; T. Sauer; C. Smeenk; J. Stachel; M. Wazeck; and D. WA1/4nsch.

With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schroedinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory supplemented by many concrete examples for a great variety of noncompact semisimple Lie algebras and groups. Contents: Introduction Lie Algebras and Groups Real Semisimple Lie Algebras Invariant Differential Operators Case of the Anti-de Sitter Group Conformal Case in 4D Kazhdan-Lusztig Polynomials, Subsingular Vectors, and Conditionally Invariant Equations Invariant Differential Operators for Noncompact Lie Algebras Parabolically Related to Conformal Lie Algebras Multilinear Invariant Differential Operators from New Generalized Verma Modules Bibliography Author Index Subject Index

This book presents lecture materials from the Third LOFAR Data School, transformed into a coherent and complete reference book describing the LOFAR design, along with descriptions of primary science cases, data processing techniques, and recipes for data handling. Together with hands-on exercises the chapters, based on the lecture notes, teach fundamentals and practical knowledge. LOFAR is a new and innovative radio telescope operating at low radio frequencies (10-250 MHz) and is the first of a new generation of radio interferometers that are leading the way to the ambitious Square Kilometre Array (SKA) to be built in the next decade. This unique reference guide serves as a primary information source for research groups around the world that seek to make the most of LOFAR data, as well as those who will push these topics forward to the next level with the design, construction, and realization of the SKA. This book will also be useful as supplementary reading material for any astrophysics overview or astrophysical techniques course, particularly those geared towards radio astronomy (and radio astronomy techniques).

This book is for physicists, historians and philosophers of physics as well as students seeking an introduction to ongoing debates in relativistic and quantum physics. This title covers the recent debates on the emergence of relativity and quantum theory. It includes chapters with an introductory character, comprehensible to students and science teachers. It strengthens the bonds between the communities of scientists, historians, and philosophers.

What is Time? Assuming no prior specialized knowledge by the reader, the book raises specific, hitherto overlooked questions about how time works, such as how and why anyone can be made to be, at the very same instant, simultaneous with events that are actually days apart. It examines abiding issues in the physics of time or at its periphery which still elude a full explanation such as delayed choice experiments, the brain's perception of time during saccadic masking, and more and suggests that these phenomena can only exist because they ultimately obey applicable mathematics, thereby agreeing with a modern view that the universe and everything within it, including the mind, are ultimately mathematical structures. It delves into how a number of conundrums, such as the weak Anthropic Principle, could be resolved, and how such resolutions could be tested experimentally. All its various threads converge towards a same new vision of the ultimate essence of time, seen as a side effect from a deeper reality.

Spinors are used extensively in physics. It is widely accepted that they are more fundamental than tensors, and the easy way to see this is through the results obtained in general relativity theory by using spinors -- results that could not have been obtained by using tensor methods only.

The foundation of the concept of spinors is groups; spinors appear as representations of groups. This textbook expounds the relationship between spinors and representations of groups. As is well known, spinors and representations are both widely used in the theory of elementary particles.

The authors present the origin of spinors from representation theory, but nevertheless apply the theory of spinors to general relativity theory, and part of the book is devoted to curved space-time applications.

Based on lectures given at Ben Gurion University, this textbook is intended for advanced undergraduate and graduate students in physics and mathematics, as well as being a reference for researchers.

Relativistic quantum electrodynamics, which describes the electromagnetic interactions of electrons and atomic nuclei, provides the basis for modeling the electronic structure of atoms, molecules and solids and of their interactions with photons and other projectiles. The theory underlying the widely used GRASP relativistic atomic structure program, the DARC electron-atom scattering code and the new BERTHA relativistic molecular structure program is presented in depth, together with computational aspects relevant to practical calculations. Along with an understanding of the physics and mathematics, the reader will gain some idea of how to use these programs to predict energy levels, ionization energies, electron affinities, transition probabilities, hyperfine effects and other properties of atoms and molecules. It is intended for Physicists and Chemists who need to understand the theory of atomic and molecular structure and processes.

This monograph presents a self contained mathematical treatment of the initial value problem for shock wave solutions of the Einstein equations in General Relativity. It has a clearly outlined goal: proving a certain local existence theorem. Concluding remarks are added and commentary is provided throughout. The author is a well regarded expert in this area.

The purpose of this book is to give a systematic pedagogical exposition of the quantitative analysis of Wilson lines and gauge-invariant correlation functions in quantum chromodynamics. Using techniques from the previous volume (Wilson Lines in Quantum Field Theory, 2014), an ab initio methodology is developed and practical tools for its implementation are presented. Emphasis is put on the implications of gauge invariance and path-dependence properties of transverse-momentum dependent parton density functions. The latter are associated with the QCD factorization approach to semi-inclusive hadronic processes, studied at currently operating and planned experimental facilities. Contents: Introduction Particle Number Operators in Quantum Mechanics and in Quantum Field Theory Geometry of Quantum Field Theories Basics of Wilson Lines in QCD Gauge-Invariant Parton Densities Simplifying Wilson Line Calculations Brief Literature Guide Conventions and Reference Formulae Integrations Bibliography Index

Dark Energy and Dark Matter are among the greatest mysteries in modern cosmology. The present work explores in depth how large cosmic structures can help us unveil the nature of these components of the Universe. One the one hand, it focuses on a signature that Dark Energy imprints on the Cosmic Microwave Background through its impact on the time-evolution of gravitational potentials: the integrated Sachs-Wolfe (iSW) effect. Another cosmological background, the Cosmic Infrared Background, is considered for the first time in the study of the iSW effect and demonstrated to be a highly efficient and promising tracer. Changing the perspective on the problem, the use of superstructures for iSW detection is then extensively reviewed: using precise solutions to Einstein's general relativity equations, the full iSW effect is computed, especially due to the cosmic voids predicted by the theory. Using measurements from the most recent data, it is subsequently shown how the iSW probes the solidity of the cosmological standard model. On the topic of Dark Matter, an original study is presented, showing that temperature measurements of the intergalactic medium shed light on the nature of Dark Matter particles, providing the tightest constraints on their decay properties.

Many large-scale projects for detecting gravitational radiation are currently being developed, all with the aim of opening a new window onto the observable Universe. As a result, numerical relativity has recently become a major field of research, and Elements of Numerical Relativity and Relativistic Hydrodynamics is a valuable primer for both graduate students and non-specialist researchers wishing to enter the field.

A revised and significantly enlarged edition of LNP 673 Elements of Numerical Relativity, this book starts with the most basic insights and aspects of numerical relativity before it develops coherent guidelines for the reliable and convenient selection of each of the following key aspects: evolution formalism; gauge, initial, and boundary conditions; and various numerical algorithms. And in addition to many revisions, it includes new, convenient damping terms for numerical implementations, a presentation of the recently-developed harmonic formalism, and an extensive, new chapter on matter space-times, containing a thorough introduction to relativistic hydrodynamics.

While proper reference is given to advanced applications requiring large computational resources, most tests and applications in this book can be performed on a standard PC.