This textbook on Feynman integrals starts from the basics, requiring only knowledge of special relativity and undergraduate mathematics. Feynman integrals are indispensable for precision calculations in quantum field theory. At the same time, they are also fascinating from a mathematical point of view. Topics from quantum field theory and advanced mathematics are introduced as needed. The book covers modern developments in the field of Feynman integrals. Topics included are: representations of Feynman integrals, integration-by-parts, differential equations, intersection theory, multiple polylogarithms, Gelfand-Kapranov-Zelevinsky systems, coactions and symbols, cluster algebras, elliptic Feynman integrals, and motives associated with Feynman integrals. This volume is aimed at a) students at the master's level in physics or mathematics, b) physicists who want to learn how to calculate Feynman integrals (for whom state-of-the-art techniques and computations are provided), and c) mathematicians who are interested in the mathematical aspects underlying Feynman integrals. It is, indeed, the interwoven nature of their physical and mathematical aspects that make Feynman integrals so enthralling.

This book provides advanced students and postdocs, as well as current practitioners of any field of nuclear physics involving fission an understanding of the nuclear fission process. Key topics covered are: fission cross sections, fission fragment yields, neutron and gamma emission from fission and key nuclear technologies and applications where fission plays an important role. It addresses both fundamental aspects of the fission process and fission-based technologies including combining quantitative and microscopic modeling.

This BriefBook is a much extended glossary or a much condensed handbook, depending on the way one looks at it. In encyclopedic format, it covers subjects in statistics, computing, analysis, and related fields, resulting in a book that is both an introduction and a reference for scientists and engineers, especially experimental physicists dealing with data analysis.

This book provides an understandable review of SU(3) representations, SU(3) Wigner-Racah algebra and the SU(3) SO(3) integrity basis operators, which are often considered to be difficult and are avoided by most nuclear physicists. Explaining group algebras that apply to specific physical systems and discussing their physical applications, the book is a useful resource for researchers in nuclear physics. At the same time it helps experimentalists to interpret data on rotational nuclei by using SU(3) symmetry that appears in a variety of nuclear models, such as the shell model, pseudo-SU(3) model, proxy-SU(3) model, symplectic Sp(6, R) model, various interacting boson models, various interacting boson-fermion models, and cluster models. In addition to presenting the results from all these models, the book also describes a variety of statistical results that follow from the SU(3) symmetry.

The essays in this open access volume identify the key ingredients for success in capitalizing on public investments in scientific projects and the development of large-scale research infrastructures. Investment in science - whether in education and training or through public funding for developing new research tools and technologies - is a crucial priority. Authors from big research laboratories/organizations, funding agencies and academia discuss how investing in science can produce societal benefits as well as identifying future challenges for scientists and policy makers. The volume cites different ways to assess the socio-economic impact of Research Infrastructures and their role as hubs of global collaboration, creativity and innovation. It highlights the different benefits stemming from fundamental research at the local, national and global level, while also inviting us to rethink the notion of "benefit" in the 21st century. Public investment is required to maintain the pace of technological and scientific advancements over the next decades. Far from advocating a radical transformation and massive expansion in funding, the authors suggest ways for maintaining a strong foundation of science and research to ensure that we continue to benefit from the outputs. The volume draws inspiration from the first "Economics of Big Science" workshop, held in Brussels in 2019 with the aim of creating a new space for dialogue and interaction between representatives of Big Science organizations, policy makers and academia. It aspires to provide useful reading for policy makers, scientists and students of science, who are increasingly called upon to explain the value of fundamental research and adopt the language and logic of economics when engaging in policy discussions.

This book has two goals. One goal is to provide a means for those new to high-energy-density physics to gain a broad foundation from one text. The second goal is to provide a useful working reference for those in the ?eld. This book has at least four possible applications in an academic c- text. It can be used for training in high-energy-density physics, in support of the growing number of university and laboratory research groups working in this area. It also can be used by schools with an emphasis on ultrafast lasers, to provide some introduction to issues present in all laser-target - perimentswithhigh-powerlasers, andwiththoroughcoverageofthematerial in Chap. 11 on relativistic systems. In addition, it could be used by physics, applied physics, or engineering departments to provide in a single course an introduction to the basics of ?uid mechanics and radiative transfer, with d- matic applications. Finally, it could be used by astrophysics departments for a similar purpose, with the parallel bene't of training the students in the similarities and di?erences between laboratory and astrophysical systems. The notation in this text is deliberately sparse and when possible a given symbol has only one meaning. A de?nition of the symbols used is given in Appendix A. In various cases, additional subscripts are added to distinguish among cases of the same quantity, as for example in the use of ? and ? 1 2 to distinguish the mass density in two di?erent regions

Drawing on the author 's forty-plus years of experience as a researcher in the interaction of charged particles with matter, this book emphasizes the theoretical description of fundamental phenomena. Special attention is given to classic topics such as Rutherford scattering; the theory of particle stopping; the statistical description of energy loss and multiple scattering and numerous more recent developments.

This book describes the basic physical principles of atomic spectroscopy and the absorption and emission of radiation in astrophysical and laboratory plasmas. It summarizes the basics of electromagnetism and thermodynamics and then describes in detail the theory of atomic spectra for complex atoms, with emphasis on astrophysical applications. Both equilibrium and non-equilibrium phenomena in plasmas are considered. The interaction between radiation and matter is described, together with various types of radiation (e.g., cyclotron, synchrotron, bremsstrahlung, Compton). The basic theory of polarization is explained, as is the theory of radiative transfer for astrophysical applications. Atomic Spectroscopy and Radiative Processes bridges the gap between basic books on atomic spectroscopy and the very specialized publications for the advanced researcher: it will provide under- and postgraduates with a clear in-depth description of theoretical aspects, supported by practical examples of applications.

It is clear that electron transfer chemisty is now one of the most active areas of chemical study. "Advances in Electron Transfer Chemistry" has been designed to allow scientists who are developing new knowledge in this rapidly expanding area to describe their most recent research findings. This volume will serve those interested in learning about current breakthroughs in this rapidly expanding area of chemical research.

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 neutron is an elementary particle that has been extensively studied, both theoretically and experimentally. This book reviews and analyses the results of the mainly experimental research on the neutron and rationalizes what is known so far about its intrinsic properties. The book covers topics that have not previously been dealt with in detail, including the gravitational properties of the neutron, precise determination of its mass, beta-decay, and its electromagnetic properties. This translation is an updated version of the original Russian text and also covers the more recent advances made during the past 7-8 years, including the application of methods based on the storage of ultra-cold neutrons to the study of beta-decay, new precise measurement of the mass of the neutron, and confirmation of modern theories of the internal structure of the neutron.

This book describes the story of how a collaboration of several hundred physicists from Europe and North America formed in 1988 to design, construct, install, commission and operate, for the years 1995-2007 the technically innovative HERMES experiment at the DESY laboratory in Hamburg, Germany to study the spin structure of the fundamental structure of matter. The authors begin by introducing the fascinating world of subatomic physics and relate their personal story of how the HERMES experiment came about. Guided by the exciting idea to use a new type of target internal to an electron storage ring, the HERMES collaboration was born to realize this innovative experimental approach at the new HERA accelerator at DESY. The book describes the technical design of HERMES; the successful effort to secure the necessary funds to construct the experiment in different countries; the fabrication of the different components by the different HERMES institutes; and the story of the installation and commissioning of HERMES in the East Hall of HERA in the hot summer of 1995. Until 2007, when the operation of HERA ceased, the collider ran typically about 9 months per year continuously, during which HERMES data taking shifts were manned to ensure that data of the highest quality were acquired. The book describes the HERMES scientific results, their considerable impact, how HERMES shaped an entire generation of young people into scientific leaders, and ends with a description of the twenty-first century picture of the proton that has subsequently been developed.The authors played a leading role within the HERMES collaboration. They describe, using non-technical language, the various phases of the thirteen years of running, the social life in such an international collaboration, and their personal reminiscences over several decades.

This book helps dispel the notion that collective phenomena, which have become increasingly important in modern storage rings, are an obscure and inaccessible topic. The book serves as a valuable guide on how to improve synchrotrons and other storage rings. Despite an emphasis on synchrotron light sources, the basic concepts presented here are valid for other facilities as well.

Powerful new techniques, including heavy ion and exotic beams, are pushing the frontiers of nuclear physics and opening up a wealth of new fields of research. After introductory chapters on theoretical and experimental aspects of nuclear collisions and beams, Exotic Nuclear Physics'' offers articles by experienced lecturers on forefront topics in nuclear physics, such as the conquest of the neutron and the proton drip-lines, nuclear astrophysics, the equation of state of hypernuclear matter, nuclear supersymmetry and chaotic motion in nuclei. This volume continues the successful tradition of published lecture notes from the Hispalensis International Summer School. It will benefit graduate students and lecturers in search of advanced material for self-study and courses as will as researchers in search of a modern and comprehensive source of reference.

The International Conference on the History of Original Ideas and Basic Discoveries, held at the "Ettore Majorana" Centre for Scientific Culture in Erice, Sicily, July 27-August 4, 1994, brought together sixty of the leading scientists including many Nobel Laureates in high energy physics, principal contributors in other fields of physics such as high Tc superconductivity, particle accelerators and detector instrumentation, and thirty-six talented younger physicists selected from candidates throughout the world. The scientific program, including 49 lectures and a discussion session on the "Status and Future Directions in High Energy Physics" was inspired by the conference theme: The key experimental discoveries and theoretical breakthroughs of the last 50 years, in particle physics and related fields, have led us to a powerful description of matter in terms of three quark and three lepton families and four fundamental interactions. The most recent generation of experiments at e+e- and proton-proton colliders, and corresponding advances in theoretical calculations, have given us remarkably precise determinations of the basic parameters of the electroweak and strong interactions. These developments, while showing the striking internal consistency of the Standard Model, have also sharpened our view of the many unanswered questions which remain for the next generation: the origin and pattern of particle masses and families, the unification of the interactions including gravity, and the relation between the laws of physics and the initial conditions of the universe.

This book offers a comprehensive overview of the reprocessing of spent nuclear fuels, and discusses the applications of radiation, particularly spallation neutrons and gamma rays. The unspent nuclear fuel of a reactor amounts to roughly 95 per cent of the loaded fuel. It contains both fertile and fissile fuels, minor and higher actinides and radioactive fission products. In 2015, out of approximately 4 million metric tons of spent fuel, only 90,000 metric tons was reprocessed worldwide; the rest was either sent to repositories, kept for cooling down, or put on a waiting list for future reprocessing. With regard to the direct reutilization of spent nuclear fuel, the new technique of 'Energy Amplifiers' has attracted considerable attention among the nuclear energy community. Presenting extensive information on this technique, the book is divided into eight major sections: (i) spent nuclear fuel and alternative transmutation methods, (ii) general concept of accelerator-driven subcritical systems (ADSS), (iii) spallation neutron sources and the possibility of incineration, (iv) requirements for nuclear data, (v) transmutation of spent nuclear fuel and extension of the fuel cycle, (vi) spallation neutron production facilities, (vii) major experimental facilities for ADSS, and (viii) software tools for the design and modelling of ADSS. The book is ideally suited as a textbook for graduate students as well as a reference guide for researchers and practitioners.

Lattice Hadron Physics draws upon the developments made in recent years in implementing chirality on the lattice via the overlap formalism. These developments exploit chiral effective field theory in order to extrapolate lattice results to physical quark masses, new forms of improving operators to remove lattice artefacts, analytical studies of finite-volume effects in hadronic observables, and state-of-the-art lattice calculations of excited resonances. This volume, comprised of selected lectures, is designed to assist those outside the field who want quickly to become literate in these topics. As such, it provides graduate students and experienced researchers in other areas of hadronic physics with the background through which they can appreciate, if not become active in, contemporary lattice-gauge theory and its applications to hadronic phenomena.

Energy is typically regarded as understandable, despite its multiple forms of storage and transfer. Entropy, however, is an enigma, in part because of the common view that it represents disorder. That view is flawed and hides entropy's connection with energy. In fact, macroscopic matter stores internal energy, and that matter's entropy is determined by how the energy is stored. Energy and entropy are intimately linked. Energy and Entropy: A Dynamic Duo illuminates connections between energy and entropy for students, teachers, and researchers. Conceptual understanding is emphasised where possible through examples, analogies, figures, and key points. Features: Qualitative demonstration that entropy is linked to spatial and temporal energy spreading, with equilibrium corresponding to the most equitable distribution of energy, which corresponds to maximum entropy Analysis of energy and entropy of matter and photons, with examples ranging from rubber bands, cryogenic cooling, and incandescent lamps to Hawking radiation of black holes Unique coverage of numerical entropy, the 3rd law of thermodynamics, entropic force, dimensionless entropy, free energy, and fluctuations, from Maxwell's demon to Brownian ratchets, plus attempts to violate the second law of thermodynamics

This work presents some essential techniques that constitute the modern strategy for computing scattering amplitudes. It begins with an introductory chapter to fill the gap between a standard QFT course and the latest developments in the field. The author then tackles the main bottleneck: the computation of the loop Feynman integrals. The most efficient technique for their computation is the method of the differential equations. This is discussed in detail, with a particular focus on the mathematical aspects involved in the derivation of the differential equations and their solution. Ample space is devoted to the special functions arising from the differential equations, to their analytic properties, and to the mathematical techniques which allow us to handle them systematically. The thesis also addresses the application of these techniques to a cutting-edge problem of importance for the physics programme of the Large Hadron Collider: five-particle amplitudes at two-loop order. It presents the first analytic results for complete two-loop five-particle amplitudes, in supersymmetric theories and QCD. The techniques discussed here open the door to precision phenomenology for processes of phenomenological interest, such as three-photon, three-jet, and di-photon + jet production.

Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects.
Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the definition of characteristic classes, and also an introduction to complex and Kahler geometry.
Differential Geometry uses many of the classical examples from, and applications of, the subjects it covers, in particular those where closed form expressions are available, to bring abstract ideas to life. Helpfully, proofs are offered for almost all assertions throughout. All of the introductory material is presented in full and this is the only such source with the classical examples presented in detail.

If charged particles move through the interplanetary or interstellar medium, they interact with a large-scale magnetic ?eld such as the magnetic ?eld of the Sun or the Galactic magnetic ?eld. As these background ?elds are usually nearly constant in time and space, they can be approximated by a homogeneous ?eld. If there are no additional ?elds, the particle trajectory is a perfect helix along which the par- cle moves at a constant speed. In reality, however, there are turbulent electric and magnetic?elds dueto the interstellaror solar wind plasma. These ?elds lead to sc- tering of the cosmic rays parallel and perpendicular to the background ?eld. These scattering effects, which usually are of diffusive nature, can be described by s- tial diffusion coef?cients or, alternatively, by mean free paths. The knowledge of these parameters is essential for describing cosmic ray propagation as well as d- fusive shock acceleration. The latter process is responsible for the high cosmic ray energies that have been observed. The layout of this book is as follows. In Chap. 1, the general physical scenario is presented. We discuss fundamental processes such as cosmic ray propagation and acceleration in different systems such as the solar system or the interst- lar space. These processes are a consequence of the interaction between charged cosmic particles and an astrophysical plasma (turbulence). The properties of such plasmas are therefore the subject of Chap. 2.

Proceedings of a NATO ASI held in Edime, Turkey, September 5-16, 1994

Neutrons are extremely versatile probes for investigating structure and dynamics in condensed matter. Due to their large penetration depth, they are ideal for in-situ measurements of samples situated in sophisticated and advanced environments. The advent of new high-intensity neutron sources and instruments, as well as the development of new real-time techniques, allows the tracking of transformation processes in condensed matter on a microscopic scale. The present volume provides a review of the state of the art of this new and exciting field of kinetics with neutrons.

After an extensive overview of the Standard Model and of the theory and phenomenology of Supersymmetry, this book describes the recent development of the ATLAS Particle Flow algorithm, a hadronic reconstruction technique aiming at enhancing the sensitivity of the experiment to new physics through the combination of the information from different ATLAS sub-detectors. The first ever ATLAS strong SUSY search exploiting this technique is also described, reporting the results and exclusion limits obtained using the complete proton-proton collision dataset recorded by the ATLAS experiment during the second Run of the Large Hadron Collider (LHC).