UNDER THE SPELL OF THE GAUGE PRINCIPLE - by G 't HooftThe University of Bologna and its Academy of Sciences, in collaboration with the Italian National Institute for Nuclear Physics and the Italian Physical Society, celebrated in 1998 the bicentenary of a great pioneer in the field of electric phenomena - Luigi Galvani, the father of macroelectricity. During these two centuries, the physics of electric phenomena has given rise first to the Maxwell equations, then to quantum electrodynamics, and finally to the synthesis of all reproducible phenomena, the "Standard Model". A cornerstone of the Standard Model is quantum chromodynamics (QCD), which describes the interaction between quarks and gluons in the innermost part of the structure of matter.The discovery of QCD will be recalled in the future as one of the greatest achievements of mankind. Many physicists, the world over, have contributed to its creation on both the experimental and the theoretical front. Professor Antonino Zichichi has played an important role in this scientific venture, as documented by his works which are reproduced in this invaluable volume.One of the founders of European physics, Professor Victor F Weisskopf, contributes with his memories of the time when QCD had many problems. This volume owes its existence to a founding father of QCD, Professor Vladimir N Gribov, whose sudden demise prevented him from directly contributing to its final edition. Two world leaders in subnuclear theoretical physics, Professors Gerardus 't Hooft and Gabriele Veneziano, illustrate the significance of the contributions of Antonino Zichichi in QCD.

Bose-Einstein condensation of dilute gases is an exciting new field of interdisciplinary physics. The eight chapters in this volume introduce its theoretical and experimental foundations. The authors are lucid expositors who have also made outstanding contributions to the field. They include theorists Tony Leggett, Allan Griffin and Keith Burnett, and Nobel-Prize-winning experimentalist Bill Phillips. In addition to the introductory material, there are articles treating topics at the forefront of research, such as experimental quantum phase engineering of condensates, the "superchemistry" of interacting atomic and molecular condensates, and atom laser theory.

This book constitutes the proceedings of the QMath 7 Conference on Mathematical Results in Quantum Mechanics held in Prague, Czech Republic in June, 1998. The volume addresses mathematicians and physicists interested in contemporary quantum physics and associated mathematical questions, presenting new results on Schr dinger and Pauli operators with regular, fractal or random potentials, scattering theory, adiabatic analysis, and interesting new physical systems such as photonic crystals, quantum dots and wires.

Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.

This book provides an up-to-date understanding of the progress and current problems of the interplay of nonlocality in the classical theories of gravitation and quantum theory. These problems lie on the border between general relativity and quantum physics, including quantum gravity.

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.

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

"Ode to a Quantum Physicist" celebrates the scientific achievements of Marlan O. Scully on the occasion of his sixtieth birthday. It combines personal reminiscences from other renowned physicists who have known and worked with him over the years and 60+ scientific articles from the frontiers of Quantum Optics inspired by the work of M. O. Scully. The topics of these articles, published in the special volume 179 of "Optics Communications," range from classical optics via atomic physics and quantum mechanics to non-linear optics.

The book opens with special greetings from Tony Siegman, the former president of the Optical Society of America and Benjamin Bederson, the Editor-in-Chief Emeritus of "Physical Review." A long time friend, Ali Javan, dating back to Marlan's MIT days, highlights some of Marlan's scientific contributions.
Heidi Fearn's poems humanize physical phenomena and set the stage for the more personal reminiscences to come.

Friends and colleagues of Marlan from the various stages of his scientific life shed some light on his human side. These stories reflect the admiration and respect the quantum physics community holds for Marlan and bring out many humorous anecdotes of their interactions with him. Judy Scully, his wife, takes us through Marlan's youth and college years in Wyoming. Leon Cohen illuminates the Yale days and Marlan's interactions with Willis E. Lamb. Pierre Meystre describes his arrival in Tucson from
Switzerland for his first postdoctoral position with Marlan. The move from Tucson to Albuquerque is one of Suhail Zubairy's memories. Herbert Walther shines light on the impact of the multi-national Marlan and in particular, on the Max-Planck-Institut fu Quantenoptik. Wolfgang Schleich looks at his mentor
Marlan from a graduate student's point of view and opens the arena for Reesor Woodling's description of Marlan's cattle business. We conclude the trail by the article of Thomas Walther, Ed Fry and George Welsch, who bring us up to date with Marlan's activities in Texas A & M.

The actual birthday party and scientific celebration took place as a special two-day colloquium on "Modern Trends in Quantum Optics" at the Max-Planck-Institut fur Quantenoptic in Garching, Germany on June 29-30, 1999. Included in this book is the program of this meeting, as wel as some excerpts from the celebration, such as, the after dinner speech by Roy J. Glauber followed by a photo album of Marlan's life. The poems by Olga Kocharovskaya poetically describe Marlan's scientific achievements. The concluding talk by Bruce Shore, given at this meeting, begins the connection to the papers by Don Kobe, Danny Greenberger and Mark Hillary, and Shi-Yao Zhu et al. covering topics from gauge invariance via unbreakable codes to photonic band gaps. The articles from the special issue of "Optics Communications" conclude this Festschrift.

This book is on quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The time-independent QDFT constitutes a special case. The 2nd edition describes the further development of the theory, and extends it to include the presence of an external magnetostatic field. The theory is based on the 'quantal Newtonian' second and first laws for the individual electron. These laws are in terms of 'classical' fields that pervade all space, and their quantal sources. The fields are separately representative of the electron correlations that must be accounted for in local potential theory. Recent developments show that irrespective of the type of external field the electrons are subject to, the only correlations beyond those due to the Pauli exclusion principle and Coulomb repulsion that need be considered are solely of the correlation-kinetic effects. Foundational to QDFT, the book describes Schroedinger theory from the new perspective of the single electron in terms of the 'quantal Newtonian' laws. Hohenberg-Kohn density functional theory (DFT), new understandings of the theory and its extension to the presence of an external uniform magnetostatic field are described. The physical interpretation via QDFT, in terms of electron correlations, of Kohn-Sham DFT, approximations to it and Slater theory are provided.

This volume provides a sample of the present research on the foundations of quantum mechanics and related topics by collecting the papers of the Italian scholars who attended the conference entitled "The Foundations of Quantum Mechanics -- Historical Analysis and Open Questions" (Lecce, 1998). The perspective of the book is interdisciplinary, and hence philosophical, historical and technical papers are gathered together so as to allow the reader to compare different viewpoints and cultural approaches. Most of the papers confront, directly or indirectly, the objectivity problem, taking into account the positions of the founders of QM or more recent developments. More specifically, the technical papers in the book pay special attention to the interpretation of the experiments on Bell's inequalities and to decoherence theory, but topics on unsharp QM, the consistent-history approach, quantum probability and alternative theories are also discussed. Furthermore, a number of historical and philosophical papers are devoted to Planck's Weyl's and Pauli's thought, but topics such as quantum ontology, predictivity of quantum laws, etc., are also treated.

Quantum effects in macroscopic systems have long been a fascination for researchers. Over the past decade mechanical oscillators have emerged as a leading system of choice for many such experiments. The work reported in this thesis investigates the effects of the radiation-pressure force of light on macroscopic mechanical structures. The basic system studied is a mechanical oscillator that is highly reflective and part of an optical resonator. It interacts with the optical cavity mode via the radiation-pressure force. Both the dynamics of the mechanical oscillation and the properties of the light field are modified through this interaction. The experiments use quantum optical tools (such as homodyning and down-conversion) with the goal of ultimately showing quantum behavior of the mechanical center of mass motion. Of particular value are the detailed descriptions of several novel experiments that pave the way towards this goal and are already shaping the field of quantum optomechanics, in particular optomechanical laser cooling and strong optomechanical coupling.

Quantum mechanics is widely recognized as the basic law which governs all of nature, including all materials and devices. It has always been essential to the understanding of material properties, and as devices become smaller it is also essential for studying their behavior. Nevertheless, only a small fraction of graduate engineers and materials scientists take a course giving a systematic presentation of the subject. The courses for physics students tend to focus on the fundamentals and formal background, rather than on application, and do not fill the need. This invaluable text has been designed to fill the very apparent gap.The book covers those parts of quantum theory which may be necessary for a modern engineer. It focuses on the approximations and concepts which allow estimates of the entire range of properties of nuclei, atoms, molecules, and solids, as well as the behavior of lasers and other quantum-optic devices. It may well prove useful also to graduate students in physics, whose courses on quantum theory tend not to include any of these applications. The material has been the basis of a course taught to graduate engineering students for the past four years at Stanford University.Topics Discussed: Foundations; Simple Systems; Hamiltonian Mechanics; Atoms and Nuclei; Molecules; Crystals; Transitions; Tunneling; Transition Rates; Statistical Mechanics; Transport; Noise; Energy Bands; Electron Dynamics in Solids; Vibrations in Solids; Creation and Annihilation Operators; Phonons; Photons and Lasers; Coherent States; Coulomb Effects; Cooperative Phenomena; Magnetism; Shake-off Excitations; Exercise Problems.A supplementary Instructor's Solutions Manual is available for this book.

Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models in field theory and mechanics. This book is an encyclopaedia of modern geometric methods in theoretical physics. It collects together the basic mathematical facts about various types of connections, and provides a detailed exposition of relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental fields. The authors have tried to give all the necessary mathematical background, thus making the book self-contained.This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry.

Scattering of light by light is a fundamental process arising at the quantum level through vacuum fluctuations. This short book will explain how, remarkably enough, this quantum process can entirely be described in terms classical quantities. This description is derived from general principles, such as causality, unitarity, Lorentz, and gauge symmetries. The reader will be introduced into a rigorous formulation of these fundamental concepts, as well as their physical interpretation and applications.

Just as in the pervious five symposia, the aim of this symposium was to link the recent advances in technology with fundamental problems in quantum mechanics. It provided a unique interdisciplinary forum where scientists with different backgrounds were given the opportunity to discuss basic problems of common interest in quantum science and technology from various aspects. This included not only an examination of the topic in terms of quantum optics and mesoscopic physics, but also in terms of the physics of precise measurement, macroscopic quantum phenomena, complex systems, and other fundamental problems in quantum physics. Two new important fields were also dealt with - the field of quantum computing, including quantum teleportation, quantum information, and cryptography, and the field of laser cooling, including Bose-Einstein condensation and atom interferometry. The resulting proceedings will be welcomed both as a good introductory book on quantum coherence and decoherence by newcomers to the field and as a reference book for experts in this dynamic area.

Building on the foundations laid in his Introduction to Superstrings and M Theory, Professor Kaku discusses such topics as the classification of conformal string theories, knot theory, the Yang-Baxter relation, quantum groups, and the insights into 11-dimensional strings recently obtained from M-theory. New chapters discuss such topics as Seiberg-Witten theory, M theory and duality, and D-branes. Throughout, the author conveys the vitality of the current research and places readers at its forefront. Several chapters reviewing the fundamentals of string theory, making the presentation of the material self-contained while keeping overlap with the earlier book to a minimum.

In recent years, there has been tremendous progress on the interface of geometry and mathematical physics. This book reflects the expanded articles of several lectures in these areas delivered at the University of Adelaide, with an audience of primarily graduate students. The aim of this volume is to provide surveys of recent progress without assuming too much prerequisite knowledge and with a comprehensive bibliography, so that researchers and graduate students in geometry and mathematical physics will benefit. The contributors cover a number of areas in mathematical physics. Chapter 1 offers a self-contained derivation of the partition function of Chern-Simons gauge theory in the semiclassical approximation. Chapter 2 considers the algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory, including their relation to the braid group, quantum groups and infinite dimensional Lie algebras. Chapter 3 surveys the application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems. Chapter 4 examines the variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds. Chapter 5 is a review of monopoles in non-Abelian gauge theories and the various approaches to understanding them. Chapter 6 covers much of the exciting recent developments in quantum cohomology, including relative Gromov-Witten invariant, birational geometry, naturality and mirror symmetry. Chapter 7 explains the physics origin of the Seiberg-Witten equations in four-manifold theory and a number of important concepts in quantum field theory, such asvacuum, mass gap, (super)symmetry, anomalies and duality. Contributors: D.H. Adam, P. Bouwknegt, A.L. Carey, A. Harris, E. Langmann, M.K. Murray, Y. Ruan, S. Wu D. H. Adams: Semiclassical Approximation in Chern-Simons Gauge Theory P. Bouwknegt: The Knizhnik-Zamolodchikov Equations A. L. Carey and E. Langmann: Loop Groups and Quantum Fields A. Harris: Some Applications of Variational Calculus in Hermitian Geometry M. K. Murray: Monopoles Y. Ruan: On Gromov-Witten Invariants and Quantum Cohomology S. Wu The Geometry and Physics of the Seiberg-Witten Equations

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.

Visual Quantum Mechanics is a systematic effort to investigate and to teach quantum mechanics with the aid of computer-generated animations. Although it is self-contained, this book is part of a two-volume set on Visual Quantum Mechanics. The first book appeared in 2000, and earned the European Academic Software Award in 2001 for oustanding innovation in its field. While topics in book one mainly concerned quantum mechanics in one- and two-dimensions, book two sets out to present three-dimensional systems, the hydrogen atom, particles with spin, and relativistic particles. Together the two volumes constitute a complete course in quantum mechanics that places an emphasis on ideas and concepts, with a fair to moderate amount of mathematical rigor.

The material for these volumes has been selected from the past twenty years' examination questions for graduate students at University of California at Berkeley, Columbia University, University of Chicago, MIT, State University of New York at Buffalo, Princeton University and University of Wisconsin.

"Is quantum logic really logic?" This book argues for a positive answer to this question once and for all. There are many quantum logics and their structures are delightfully varied. The most radical aspect of quantum reasoning is reflected in unsharp quantum logics, a special heterodox branch of fuzzy thinking.
For the first time, the whole story of Quantum Logic is told; from its beginnings to the most recent logical investigations of various types of quantum phenomena, including quantum computation. Reasoning in Quantum Theory is designed for logicians, yet amenable to advanced graduate students and researchers of other disciplines.

This textbook covers a broad spectrum of developments in QFT, emphasizing those aspects that are now well consolidated and for which satisfactory theoretical descriptions have been provided. The book is unique in that it offers a new approach to the subject and explores many topics merely touched upon, if covered at all, in standard reference works. A detailed and largely non-technical introductory chapter traces the development of QFT from its inception in 1926. The elegant functional differential approach put forward by Schwinger, referred to as the quantum dynamical (action) principle, and its underlying theory are used systematically in order to generate the so-called vacuum-to-vacuum transition amplitude of both abelian and non-abelian gauge theories, in addition to Feynman's well-known functional integral approach, referred to as the path-integral approach. Given the wealth of information also to be found in the abelian case, equal importance is put on both abelian and non-abelian gauge theories. Particular emphasis is placed on the concept of a quantum field and its particle content to provide an appropriate description of physical processes at high energies, where relativity becomes indispensable. Moreover, quantum mechanics implies that a wave function renormalization arises in the QFT field independent of any perturbation theory - a point not sufficiently emphasized in the literature. The book provides an overview of all the fields encountered in present high-energy physics, together with the details of the underlying derivations. Further, it presents "deep inelastic" experiments as a fundamental application of quantum chromodynamics. Though the author makes a point of deriving points in detail, the book still requires good background knowledge of quantum mechanics, including the Dirac Theory, as well as elements of the Klein-Gordon equation. The present volume sets the language, the notation and provides additional background for reading Quantum Field Theory II - Introduction to Quantum Gravity, Supersymmetry and String Theory, by the same author. Students in this field might benefit from first reading the book Quantum Theory: A Wide Spectrum (Springer, 2006), by the same author.

This fifteenth volume of the Poincare Seminar Series, Dirac Matter, describes the surprising resurgence, as a low-energy effective theory of conducting electrons in many condensed matter systems, including graphene and topological insulators, of the famous equation originally invented by P.A.M. Dirac for relativistic quantum mechanics. In five highly pedagogical articles, as befits their origin in lectures to a broad scientific audience, this book explains why Dirac matters. Highlights include the detailed "Graphene and Relativistic Quantum Physics", written by the experimental pioneer, Philip Kim, and devoted to graphene, a form of carbon crystallized in a two-dimensional hexagonal lattice, from its discovery in 2004-2005 by the future Nobel prize winners Kostya Novoselov and Andre Geim to the so-called relativistic quantum Hall effect; the review entitled "Dirac Fermions in Condensed Matter and Beyond", written by two prominent theoreticians, Mark Goerbig and Gilles Montambaux, who consider many other materials than graphene, collectively known as "Dirac matter", and offer a thorough description of the merging transition of Dirac cones that occurs in the energy spectrum, in various experiments involving stretching of the microscopic hexagonal lattice; the third contribution, entitled "Quantum Transport in Graphene: Impurity Scattering as a Probe of the Dirac Spectrum", given by Helene Bouchiat, a leading experimentalist in mesoscopic physics, with Sophie Gueron and Chuan Li, shows how measuring electrical transport, in particular magneto-transport in real graphene devices - contaminated by impurities and hence exhibiting a diffusive regime - allows one to deeply probe the Dirac nature of electrons. The last two contributions focus on topological insulators; in the authoritative "Experimental Signatures of Topological Insulators", Laurent Levy reviews recent experimental progress in the physics of mercury-telluride samples under strain, which demonstrates that the surface of a three-dimensional topological insulator hosts a two-dimensional massless Dirac metal; the illuminating final contribution by David Carpentier, entitled "Topology of Bands in Solids: From Insulators to Dirac Matter", provides a geometric description of Bloch wave functions in terms of Berry phases and parallel transport, and of their topological classification in terms of invariants such as Chern numbers, and ends with a perspective on three-dimensional semi-metals as described by the Weyl equation. This book will be of broad general interest to physicists, mathematicians, and historians of science.

This book is an introduction to the two closely related subjects of quantum optics and quantum information. The book gives a simple, self-contained introduction to both subjects, while illustrating the physical principles of quantum information processing using quantum optical systems. To make the book accessible to those with backgrounds other than physics, the authors also include a brief review of quantum mechanics. Furthermore, some aspects of quantum information, for example those pertaining to recent experiments on cavity QED and quantum dots, are described here for the first time in book form.