"Visual Quantum Mechanics" uses the computer-generated animations found on the accompanying material on Springer Extras to introduce, motivate, and illustrate the concepts explained in the book. While there are other books on the market that use Mathematica or Maple to teach quantum mechanics, this book differs in that the text describes the mathematical and physical ideas of quantum mechanics in the conventional manner. There is no special emphasis on computational physics or requirement that the reader know a symbolic computation package. Despite the presentation of rather advanced topics, the book requires only calculus, making complicated results more comprehensible via visualization. The material on Springer Extras provides easy access to more than 300 digital movies, animated illustrations, and interactive pictures. This book along with its extra online materials forms a complete introductory course on spinless particles in one and two dimensions.

The author develops a novel analysis method for QCD sum rules (QCDSR) by applying the maximum entropy method (MEM) to arrive at an analysis with less artificial assumptions than previously held. This is a first-time accomplishment in the field. In this thesis, a reformed MEM for QCDSR is formalized and is applied to the sum rules of several channels: the light-quark meson in the vector channel, the light-quark baryon channel with spin and isospin 1/2, and several quarkonium channels at both zero and finite temperatures. This novel technique of combining QCDSR with MEM is applied to the study of quarkonium in hot matter, which is an important probe of the quark-gluon plasma currently being created in heavy-ion collision experiments at RHIC and LHC.

This Brief presents an introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics. Emphasis is placed on gaining a physical understanding of the running of the couplings. The Wilsonian version of the renormalization group is related to conventional perturbative calculations with dimensional regularization and minimal subtraction. An introduction is given to some of the remarkable renormalization group properties of supersymmetric theories.

This book presents recent results of basic research in the field of Raman scattering by optic and acoustic phonons in semiconductors, quantum wells and superlattices. It also describes various new applications for analytical materials research which have emerged alongside with scientific progress. Trends in Raman techniques and instrumentation and their implications for future developments are illustrated.

If a heavy particle ion (atom, molecule, muon) collides with another in the gas phase at speeds approaching the speed of light, the time-dependent Dirac equation equation must be used for its description, including quantum electro-dynamic, special relativity and magnetic coupling effects. In this book we study one electron in the variety of rearrangement collisions: radiative and non-radiative capture, ionization, capture by pair (one electron, one positron) production and antihydrogen production. Our relativistic continuum distorted-wave theory accounts extremely well for the simultaneous behaviour of the electron with respect to the nuclear charges of the projectile and the target. This is the first book developed in this subject. Containing many diagrams and tables, and fully referenced, it goes beyond chapters in previous books. The relativistic continuum distorted-wave theory developed by the authors group, is shown to be fully Hermitean. Detailed mathematics are provided in nine appendices.

The present work is the first volume of a substantially enlarged version of the mimeographed notes of a course of lectures first given by me in the Indian Statistical Institute, Calcutta, India, during 1964-65. When it was suggested that these lectures be developed into a book, I readily agreed and took the opportunity to extend the scope of the material covered. No background in physics is in principle necessary for understand ing the essential ideas in this work. However, a high degree of mathematical maturity is certainly indispensable. It is safe to say that I aim at an audience composed of professional mathematicians, advanced graduate students, and, hopefully, the rapidly increasing group of mathematical physicists who are attracted to fundamental mathematical questions. Over the years, the mathematics of quantum theory has become more abstract and, consequently, simpler. Hilbert spaces have been used from the very beginning and, after Weyl and Wigner, group representations have come in conclusively. Recent discoveries seem to indicate that the role of group representations is destined for further expansion, not to speak of the impact of the theory of several complex variables and function-space analysis. But all of this pertains to the world of interacting subatomic particles; the more modest view of the microscopic world presented in this book requires somewhat less. The reader with a knowledge of abstract integration, Hilbert space theory, and topological groups will find the going easy."

'Quantum mechanics for real. This is the good stuff, the most mysterious aspects of how reality works, set out with crystalline clarity. The place to start' Sean Carroll, physicist, California Institute of Technology, author of The Particle at the End of the Universe This is the ultimate practical introduction to quantum mechanics. World-renowned physicist Leonard Susskind and data engineer Art Friedman give you the basic skills you need to tackle this famously difficult topic yourself. They provide clear, lively explanations of basic concepts, introduce the key fields of quantum mechanics and include step-by-step exercises. Making a complex subject 'as simple as possible, but no simpler', this is a practical toolkit for amateur scientists that you won't find anywhere else.

In the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming "the "quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory's unresolved issues will get solved along the way. However, these fundamental issues may need to be solved before attempting to define a quantum theory of gravity.
The present text adopts this point of view, addressing the following basic questions: What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory?
A possible way to overcome critical issues in present-day quantum physics - such as "a priori "assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility of talking about systems without reference to an external observer - is through a reformulation of quantum theory in terms of a different mathematical framework called topos theory.
This course-tested primer sets out to explain to graduate students and newcomers to the field alike, the reasons for choosing topos theory to resolve the above-mentioned issues and how it brings quantum physics back to looking more like a "neo-realist" classical physics theory again.

In these volumes, the most significant of the collected papers of the Chinese-American theoretical physicist Tsung-Dao Lee are printed. A complete list of his published papers, in order of publication, appears in the Bibliography of T.D. Lee. The papers have been arranged into ten categories, in most cases according to the subject matter. At the beginning of each of the first eight categories of papers, there is a commentary on the content and significance of all of the papers in the category. The two short final categories do not have any commentaries. The editor would like to thank Dr. Richard Friedberg for his assistance in the early stages of the editorial work on this project, as well as for writing commentaries on the papers of Categories III and IV. I would also like to thank Dr. Norman Christ for writing the commentary on the papers of Category VII. The assistance of Irene Tramm was in- valuable in many aspects of preparing this collection, including locating copies of Lee's papers. GERALD FEINBERG List of Categories of T.D. Lee's Papers Volume 1 I. Weak Interactions II. Early Papers on Astrophysics and Hydrodynamics III. Statistical Mechanics IV. Polarons and Solitons Volume 2 V. Quantum Field Theory VI. Symmetry Principles Volume 3 VII. Discrete Physics VIII. Strong Interaction Models IX. Historical Papers X. Gravity (Continuum Theory) Contents (Volume 1)* Introduction (by G. Feinberg) ............................................................ xi Bibliography of T.D. Lee ................................................................. xv I. Weak Interactions Commentary ................................................................... .

This collection of lectures and essays by eminent researchers in the field, many of them nobel laureates, is an outgrow of a special event held at CERN in late 2009, coinciding with the start of LHC operations. Careful transcriptions of the lectures have been worked out, subsequently validated and edited by the lecturers themselves. This unique insight into the history of the field includes also some perspectives on modern developments and will benefit everyone working in the field, as well as historians of science.

Why writing a book about a specialized task of the large topic of complex systems? And who will read it? The answer is simple: The fascination for a didactically valuable point of view, the elegance of a closed concept and the lack of a comprehensive disquisition.

The fascinating part is that field equations can have localized solutions exhibiting the typical characteristics of particles. Regarding the field equations this book focuses on, the field phenomenon of localized solutions can be described in the context of a particle formalism, which leads to a set of ordinary differential equations covering the time evolution of the position and the velocity of each particle. Moreover, starting from these particle dynamics and making the transition to many body systems, one considers typical phenomena of many body systems as shock waves and phase transitions, which themselves can be described as field phenomena. Such transitions between different level of modelling are well known from conservative systems, where localized solutions of quantum field theory lead to the mechanisms of elementary particle interaction and from this to field equations describing the properties of matter. However, in dissipative systems such transitions have not been considered yet, which is adjusted by the presented book. The elegance of a closed concept starts with the observation of self-organized current filaments in a semiconductor gas discharge system. These filaments move on random paths and exhibit certain particle features like scattering or the formation of bound states. Neither the reasons for the propagation of the filaments nor the laws of the interaction between the filaments can be registered by direct observations. Therefore a model is established, which is phenomenological in the first instance due to the complexity of the experimental system. This model allows to understand the existence of localized structures, their mechanisms of movement, and their interaction, at least, on a qualitative level. But this model is also the starting point for developing a data analysis method that enables the detection of movement and interaction mechanisms of the investigated localized solutions. The topic is rounded of by applying the data analysis to real experimental data and comparing the experimental observations to the predictions of the model.

A comprehensive publication covering the interesting topic of localized solutions in reaction diffusion systems in its width and its relation to the well known phenomena of spirals and patterns does not yet exist, and this is the third reason for writing this book. Although the book focuses on a specific experimental system the model equations are as simple as possible so that the discussed methods should be adaptable to a large class of systems showing particle-like structures.

Therefore, this book should attract not only the experienced scientist, who is interested in self-organization phenomena, but also the student, who would like to understand the investigation of a complex system on the basis of a continuous description.

Divided into four parts, this book covers recent developments in topics pertaining to gravity theories, including discussions on the presence of scalar fields. Part One is devoted to exact solutions in general relativity, and is mainly concerned with the results of rotating null dust beams and fluids. Also included is a panoramic vision of new research directions in this area, which would require revising certain theorems and their possible extensions within gravity theories, new aspects concerning the Ernst potentials, double Kerr spacetimes, and rotating configurations. In particular, there is a detailed discussion of totally symmetric and totally geodesic spaces, in which a method for generating (2+1)-dimensional solutions from (3+1)-dimensional solutions is given. Part Two deals with alternative theories of gravity, all of which include scalar fields and gauge fields. Here, quantum and cosmological effects, which arise from both gravity theories in four and higher dimensions and from metric-affine theories, are investigated. Part Three is devoted to cosmological and inflationary scenarios. Local effects, such as the influence of scalar fields in protogalactic interactions, numerical studies of the collapse of molecular cores, as well as the inverse inflationary problem and the blue eigenvalue spectrum of it, are considered. Moreover, the role of scalar fields as dark matter and quantum cosmology in the Bergman-Wagoner and Gowdy theories, together with the relation of the conformal symmetry and deflationary gas universe, are likewise presented. The last part of the book includes some mixed topics which are still in the experimental stage. Among them are the foundation of the Maxwell theory, a discussion on electromagnetic Thirring problems, a note on the staticity of black holes with non-minimally coupled scalar fields, and a study of the Lorentz force free charged fluids in general relativity. Thus, this book is the most up-to-date, comprehensive collection of papers on the subject of exact solutions and scalar fields in gravity and is a valuable tool for researchers in the area.

Based on the Fourth International Conference on Quantum Communication, Measurement and Computing, this volume brings together scientists working in the interdisciplinary fields of quantum communication science and technology. Topics include quantum information theory, quantum computing, stochastic processes and filtering, and quantum measurement theory

The Shaggy Steed is an unassuming figure from Irish folklore who reveals himself as an inspiring teacher of the forces hidden in the universe. This book celebrates an unassuming bit of physics that also turns out to be an inspiring teacher. The two-body problem - the motion of two bodies bound by the inverse-square force of gravity and electricity - is the Shaggy Steed of physics, guiding the reader to an understanding of both the forces and the mathematical beauty hidden in the physical world.

An exploration of the intersection of particle physics, astrophysics, and cosmology known as astroparticle physics. Extreme electromagnetic conditions present in puslars and other stars allow for investigations of the role of quantum processes in the dynamics of astrophysical objects and in the early Universe. Based in part on the authors' own work, this book systematically describes several methods of calculation of the effects of strong electromagnetic fields in quantum processes using analytical solutions of the Dirac equation and Feynmann diagrams at both the loop and tree levels. The consideration is emphasized at the two limiting cases: the case of a very strong magnetic field, and the case of a crossed field. The presentation will appeal to graduate students of theoretical physics with prior understanding of Quantum Field Theory (QFT) and the Standard Model of Electroweak Interactions, as well as specialists in QFT wishing to know more about the problems of quantum phenomena in external electomagnetic fields.

th The 29 International Conference was held as the first one of the millennium at its Fort Lauderdale venue. These conferences began, with High Energy Physics being the main topic, by introducing gradually cosmology into its programs. These proceedings of the 2000 conference reflect the variety of topics and ideas discussed. Our future conferences will be designed somewhat akin to the early Coral Gables Conferences where we shall seek some convergence of ideas. For this reason various committees have been formed from among the participating physicists. The committees and their memberships are listed in these proceedings. We further decided for the first time to include some graduate student participants in our future meetings for which also a committee has already been established. The topics will demonstrate a more activist structure of the Coral Gables Conferences, for example the duality of the gravitational forces and expansion of the universe will be discussed from this point of view since it conveys a convergence to the ideas of quintessence versus the ordinary theory, which are considered as the cause of the expansion of the universe. We further wish to announce that the future conferences will assume a collective organization where several committees as listed in these proceedings will have their input into the conference. We have now introduced new topics and ideas, which referred especially to the attractive and repulsive nature of the gravitational force. These proceedings of the conference contain a variety of topics and ideas.

Review articles on three topics of considerable current interest make up the present volume. The first, on A-hypernuclei, was solicited by the editors in order to provide nuclear physicists with a general description of the most recent developments in a field which this audience has largely neglected or, perhaps, viewed as a novelty in which a bizarre nuclear system gave some information about the lambda-nuclear intersection. That view was never valid. The very recent developments reviewed here-particularly those pertaining to hypernuclear excitations and the strangeness exchange reactions-emphasize that this field provides important information about the models and central ideas of nuclear physics. The off-shell behavior of the nucleon-nucleon interaction is a topic which was at first received with some embarrassment, abuse, and neglect, but it has recently gained proper attention in many nuclear problems. Interest was first focused on it in nuclear many-body theory, but it threatened nuclear physicists'comfortable feeling about nonrelativistic potential theory, and many no doubt hoped that it would remain merely an esoteric diversion within the many-body cult. In the editors' opinion, this subject is now emi nently respectable and a review of it indeed timely. The third topic, nuclear charge distributions, is one which almost every nuclear physicist believed had been weIl in hand for some years."

During the decade there were many developments in laser research and numerous applications of the laser were made in fields of science and engineering. Many theoretical and experimental ad vances were made in the Soviet Union; often they paralleled those taking place in the United States and elsewhere but started from different points, proceeded along different paths, and yielded dif ferent insights into the physical processes taking place in the la ser. The present book offers a unified theory of lasers by which the operating characteristics of the laser are described and re lated to the details of the radiation emitted. Extensive emenda tions to the original, Soviet edition were supplied by the author and incorporated into the text, and references to the English literature were added to the translation to permit the reader to readily ex plore topics in greater detail. Since the Soviet edition's appearance in 1968 one very impor tant area has developed-that of mode locking and picosecond pulse production. This area is so important that no comprehensive work on the laser published in 1972 could neglect it. Accordingly, Chap ter XII was added to round off the treatment. I am indebted to my colleague, Professor A. J. Carruthers of the University of Min nesota for many illuminating discussions on mode locking."

In this text the author gives a rather complete account of the available experimental information on neutral current reactions as predicted by the standard theory of electroweak interactions. The data, which range from atomic parity violation to the discovery of the W and Z bosons, impressively support the theory as formulated by Glashow, Weinberg and Salam. The experimental data are critically reviewed and related to the standard theory, whose formal essentials are presented in a transparent way. A complete compilation is given of precision measurements of the Weinberg angle. Special attention is paid to high energy electron-positron experiments at PEP and PETRA leading to the most precise value of the Weinberg angle so far made from such experiments. Latest results from the high-statistics deep-inelastic neutrino scattering experiments have been included along with recent measurements of neutrino electron scattering, data and analysis for polarized-electron nucleon scattering, polarized-muon scattering, atomic parity violation and proton-antiproton experiments establishing the nature of the intermediate bosons.

The XII Max Born Symposium has a special character. It was held in honour th of Jan Lopusza nski on the occasion of his 75 birthday. As a rule the Max Born Symposia organized by the Institute of Theoretical Physics at the University of Wroc law were devoted to well-de ned subjects of contemporary interest. This time, however, the organizers decided to make an exception. Lopusza nski's in?uence on and contribution to the development of th- retical physics at Wrocla w University is highly appreciable. His personality and scienti c achievements gave him authority which he used to the best - vantage of the Institute. In fact we still pro t from his knowledge, experience and judgment. Lopusza nski's scienti c activity extended over about half a century. He successfully participated in research on the most important and fascinating issues of theoretical physics. During his scienti c career he met and made friends with many outstanding physicists who shaped theoretical physics to the present form. For this reason, as well as the coincidence of the approaching end of the century, we thought that it would be interesting and instructive to give the symposium a retrospective character. We decided to trust the speakers' judgment and intuition for the choice of subjects for their talks. We just asked them to give the audience the important message based on their knowledge and experience.

This volume explores multiscale methods as applied to various areas of physics and to the relative developments in mathematics. In the last few years, multiscale methods have lead to spectacular progress in our understanding of complex physical systems and have stimulated the development of very refined mathematical techniques. At the same time on the experimental side, equally spectacular progress has been made in developing experimental machinery and techniques to test the foundations of quantum mechanics.

The Workshop N* Physics and non-perturbative QeD was held at the Eu ropean Center for Theoretical Studies and Related Areas (ECT*) in Trento, Italy, during May 18-29, 1998. Previous workshops of the series on N* Physics took place at the Florida State University (1994), at CEBAF (1995), at the Institute for Nuclear Theory in Seattle (1996) and at the George Washington University (1997). The Workshop was devoted to a summary of recent experimental and the oretical research on N* phsyics and special emphasis was given to the infor mation that photo-and electro-production of nucleon resonances can provide on the non-perturbative regime of Quantum Chromodynamics. The idea was to stimulate discussions among experimentalists and theoreticians in order to pursue the interpretation of the huge amount of forthcoming data from several laboratories in the world. It was therefore decided to have both experimental and theoretical lectures on the main topics, like, among the others, single and double pion production, TJ-and K-meson production, the GDH sum rule, the spin of the proton, etc. Thanks to the unusual two-week extension of the Work shop, the allotted time for the lectures was extended up to one hour in order to allow the invited lecturers to give a detailed presentation of their topics. Fi nally, various short contributions were selected to sharpen the discussion about selected items."

This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems. It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive dynamics, relativistic quantum information, and a new paradigm for quantum computation beyond the usual quantum Turing machine. Also, some important applications of information theory to genetics and life sciences, as well as recent experimental and theoretical discoveries in quantum photosynthesis are described.

In this book the author presents two important findings revealed by high-precision magnetic penetration depth measurements in iron-based superconductors which exhibit high-transition temperature superconductivity up to 55 K: one is the fact that the superconducting gap structure in iron-based superconductors depends on a detailed electronic structure of individual materials, and the other is the first strong evidence for the presence of a quantum critical point (QCP) beneath the superconducting dome of iron-based superconductors. The magnetic penetration depth is a powerful probe to elucidate the superconducting gap structure which is intimately related to the pairing mechanism of superconductivity. The author discusses the possible gap structure of individual iron-based superconductors by comparing the gap structure obtained from the penetration depth measurements with theoretical predictions, indicating that the non-universal superconducting gap structure in iron-pnictides can be interpreted in the framework of A1g symmetry. This result imposes a strong constraint on the pairing mechanism of iron-based superconductors. The author also shows clear evidence for the quantum criticality inside the superconducting dome from the absolute zero-temperature penetration depth measurements as a function of chemical composition. A sharp peak of the penetration depth at a certain composition demonstrates pronounced quantum fluctuations associated with the QCP, which separates two distinct superconducting phases. This gives the first convincing signature of a second-order quantum phase transition deep inside the superconducting dome, which may address a key question on the general phase diagram of unconventional superconductivity in the vicinity of a QCP.