In this second edition, the following recent papers have been added: "Gauss Codes, Quantum Groups and Ribbon Hopf Algebras", "Spin Networks, Topology and Discrete Physics", "Link Polynomials and a Graphical Calculus" and "Knots Tangles and Electrical Networks". An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included.This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of knot theory, coupled with a quantum statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems.

In this second edition, the following recent papers have been added: "Gauss Codes, Quantum Groups and Ribbon Hopf Algebras", "Spin Networks, Topology and Discrete Physics", "Link Polynomials and a Graphical Calculus" and "Knots Tangles and Electrical Networks". An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included.This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of knot theory, coupled with a quantum statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems.

This text develops quantum theory from its basic assumptions, beginning with statics, followed by dynamics and details of applications and the needed computational techniques. The discussion is based on the view that the fundamental entities of the universe are not particles but fields, with the observed particles arising as their quanta. Quantum fields are thus introduced from the beginning, with a discussion of how they produce quanta that manifest themselves as particles. Most of the book, of course, deals with particle systems, as that is where most of the applications lie; the treatment of quantum field theory is confined to fundamental ideas and their consequences. For developing quantum dynamics, the author uses the Lagrangian technique with the principle of stationary action. The roots of this approach, which includes generating the canonical commutation rules, go back to a course taught by Julian Schwinger, filtered through many years of the author's own teaching. The text emphasizes that the wave function does not exist in physical three-dimensional space, but in configuration space, and it points out that the probabilistic features of the theory arise not from a lack of determinism but from the definition of the "state" of a system, so that many, though not all, of the counterintuitive aspects of quantum mechanics arise from its probabilistic nature and are shared by other probabilistic theories such as classical statistical mechanics. Intended for a graduate-level course in quantum mechanics, the treatment assumes a knowledge of Lagrangian and Hamiltonian mechanics, Maxwell's electrodynamics, special relativity, and the elements of

This book is intended as a tutorial approach to some of the techniques used to deal with quantum dissipation and irreversibility, with special focus on their applications to the theory of measurements. The main purpose is to provide readers without a deep expertise in quantum statistical mechanics with the basic tools to develop a critical judgement on whether the major achievements in this field have to be considered a satisfactory solution of quantum paradox, or rather this ambitious achievement has to be postponed to when a new physics, more general than quantum and classical physics, will be discovered.

This book reviews recent developments of quantum Monte Carlo methods and some remarkable applications to interacting quantum spin systems and strongly correlated electron systems. It contains twenty-two papers by thirty authors. Some of the features are as follows. The first paper gives the foundations of the standard quantum Monte Carlo method, including some recent results on higher-order decompositions of exponential operators and ordered exponentials. The second paper presents a general review of quantum Monte Carlo methods used in the present book. One of the most challenging problems in the field of quantum Monte Carlo techniques, the negative-sign problem, is also discussed and new methods proposed to partially overcome it. In addition, low-dimensional quantum spin systems are studied. Some interesting applications of quantum Monte Carlo methods to fermion systems are also presented to investigate the role of strong correlations and fluctuations of electrons and to clarify the mechanism of high-Tc superconductivity. Not only thermal properties but also quantum-mechanical ground-state properties have been studied by the projection technique using auxiliary fields. Further, the Haldane gap is confirmed by numerical calculations. Active researchers in the forefront of condensed matter physics as well as young graduate students who want to start learning the quantum Monte Carlo methods will find this book useful.

This book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants were rapidly connected with quantum groups and methods in statistical mechanics. This was followed by Edward Witten's introduction of methods of quantum field theory into the subject and the formulation by Witten and Michael Atiyah of the concept of topological quantum field theories.This book is a review volume of on-going research activity. The papers derive from talks given at the Special Session on Knot and Topological Quantum Field Theory of the American Mathematical Society held at Dayton, Ohio in the fall of 1992. The book consists of a self-contained article by Kauffman, entitled Introduction to Quantum Topology and eighteen research articles by participants in the special session.This book should provide a useful source of ideas and results for anyone interested in the interface between topology and quantum field theory.

Scientific advances and several technical breakthroughs have led to a remarkable increase in available laser intensities over the past decades. In available ultra-intense laser fields, photon fluxes may become so high that free charge carriers interact coherently with several of the field's photons. In this thesis such nonlinear interactions are investigated for the prime example of radiation emission by electrons scattered from intense laser pulses of arbitrary temporal structure. To this end, nonlinear quantum field theory is employed taking the interaction with the laser into account exactly. After an in-depth introduction to classical particle dynamics as well as quantum field theory in nonlinearly intense laser fields the emission of one and two photons is explicitly analyzed. The results are then translated to viable technical applications, such as a scheme for the determination of the carrier-envelope phase of ultra-intense laser pulses and a proposal for detecting the strongly suppressed two-photon signal.

One of the most profound revolutions brought about by quantum mechanics is that it does away with the distinction between waves and particles: atoms, in particular, can exhibit all the properties that we associate with wave phenomena, such as diffraction and interference; it has recently even become possible to prepare collections of atoms in coherent states, like those of photons in a laser beam. These developments are at the core of the rapidly expanding field of atom optics. ||Atom Optics gradually leads the reader from elementary concepts to the frontiers of the field. It is organized in three parts, linear, nonlinear, and quantum atom optics. After a review of light forces on atoms and of laser cooling, the first part discusses the application of light forces to atom optical elements such as gratings, mirrors and lenses, matter-wave diffraction, and atomic traps and resonators. The discussion of nonlinear atom optics starts with a review of collisions from a viewpoint that clearly demonstrates its profound analogy with nonlinear optics. The last part, quantum atom optics, first recalls key results of many-body theory in a formulation geared specifically toward atom optics. This is followed by a discussion of atomic Bose-Einstein condensation and "atom lasers." The final chapters treat such applications as atomic solitons, four-wave mixing, superradiance, and conclude with the coherent amplification of matter waves. ||An online web component to the book, a gateway to atom optics, contains links to the leading references and journals in the field, to research sites, and to updates for the contents of the book. FROM THE REVIEWS: ¿Atom optics today has reached maturity: It has become both wave (coherent) and nonlinear atom optics. Of course that expansion required generalization in a new book. Pierre Meystre has taken just such a generalist approach in his timely ATOM OPTICS. His were the pioneering works in atom optics; to get information from the first explorer is always most valuable to the reader ¿ Recommend[ed] to all strata of the physics community.¿ ¿PHYSICS TODAY

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.

Reinvigorated by advances and insights the quantum theory of irreversible processes has recently attracted growing attention.

This volume introduces the very basic concepts of semigroup dynamics of open quantum systems and reviews a variety of modern applications. Originally published as Volume 286 (1987) in Lecture in Physics, this volume has been newly typeset, revised and corrected and also expanded to include a review on recent developments.

This book is a translation of the 8th edition of Prof. Kazuhiko Nishijima's classical textbook on quantum field theory. It is based on the lectures the Author gave to students and researchers with diverse interests over several years in Japan. The book includes both the historical development of QFT and its practical use in theoretical and experimental particle physics, presented in a pedagogical and transparent way and, in several parts, in a unique and original manner. The Author, Academician Nishijima, is the inventor (independently from Murray Gell-Mann) of the third (besides the electric charge and isospin) quantum number in particle physics: strangeness. He is also most known for his works on several other theories describing particles such as electron and muon neutrinos, and his work on the so-called Gell-Mann-Nishijima formula. The present English translation from its 8th Japanese edition has been initiated and taken care of by the editors Prof. M. Chaichian and Dr. A. Tureanu from the University of Helsinki, who were close collaborators of Prof. Nishijima. Dr. Yuki Sato, a researcher in particle physics at the University of Nagoya, most kindly accepted to undertake the heavy task of translation. The translation of the book can be regarded as a tribute to Prof. Nishijima's memory, for his fundamental contributions to particle physics and quantum field theory. The book presents with utmost clarity and originality the most important topics and applications of QFT which by now constitute the established core of the theory. It is intended for a wide circle of graduate and post-graduate students, as well as researchers in theoretical and particle physics. In addition, the book can be a useful source as a basic material or supplementary literature for lecturers giving a course on quantum field theory.

As a result of the advancements in algorithms and the huge increase in speed of computers over the past decade, electronic structure calculations have evolved into a valuable tool for characterizing surface species and for elucidating the pathways for their formation and reactivity. It is also now possible to calculate, including electric field effects, STM images for surface structures. To date the calculation of such images has been dominated by density functional methods, primarily because the computational cost of - curate wave-function based calculations using either realistic cluster or slab models would be prohibitive. DFT calculations have proven especially valuable for elucidating chemical processes on silicon and other semiconductor surfaces. However, it is also clear that some of the systems to which DFT methods have been applied have large non-dynamical correlation effects, which may not be properly handled by the current generation of Kohn-Sham-based density functionals. For example, our CASSCF calculations on the Si(001)/acetylene system reveal that at some geometries there is extensive 86 configuration mixing. This, in turn, could signal problems for DFT cal- lations on these systems. Some of these problem systems can be addressed using ONIOM or other "layering" methods, treating the primary region of interest with a CASMP2 or other multireference-based method, and treating the secondary region by a lower level of electronic structure theory or by use of a molecular mechanics method. ACKNOWLEDGEMENTS We wish to thank H. Jonsson, C. Sosa, D. Sorescu, P. Nachtigall, and T. -C."

How does the physical world interact with us? How is motion possible? What is space? What is matter? In "A Personal Journey into the Quantum World," author Jean Paul Corriveau answers fundamental questions about physics, cosmology, life, consciousness, and the afterlife and shows how quantum physics is the path to God.

Making use of basic physics, mathematics principles and simple logic, Corriveau demonstrates that the answers to these questions lie in quantum physics, which deals with objects so incredibly small the domain is beyond our imagination. Delving into the world of quantum physics, which is the root of all things, Corriveau provides theories about and debates the following questions:

What is matter?
What is space?
What is time?
Why is time relative?
What is gravitation?
How did the universe begin?
What created life?
Is there an afterlife?

Written in an easy-to-understand format and filled with graphics, "A Personal Journey into the Quantum World" addresses the role of quantum physics while raising many more intriguing questions-questions that are just as important as the answers.

This book explores the modern physicist Niels Bohr's philosophical thought, specifically his pivotal idea of complementarity, with a focus on the relation between the roles of what he metaphorically calls "spectators" and "actors." It seeks to spell out the structural and historical complexity of the idea of complementarity in terms of different modes of the 'spectator-actor' relation, showing, in particular, that the reorganization of Bohr's thought starting from his 1935 debate with Einstein and his collaborators is characterized by an extension of the dynamic conception of complementarity from non-physical contexts to the very field of quantum theory. Further, linked with this analysis, the book situates Bohr's complementarity in contemporary philosophical context by examining its intersections with post-Heideggerian hermeneutics as well as Derridean deconstruction. Specifically, it points to both the close affinities and the differences between Bohr's idea of the 'actor-spectator' relation and the hermeneutic notion of the relation between "belonging" and "distanciation."

Remarkable progress has recently been made in the application of quantumtrajectories as the computational tool for solving quantum mechanical problems. This is the first book to present these developments in the broader context of the hydrodynamical formulation of quantum dynamics. In addition to a thorough discussion of the quantum trajectory equations of motion, there is considerable material that deals with phase space dynamics, adaptive moving grids, electronic energy transfer, and trajectories for stationary states.

On the pedagogical side, a number of sections of this book will be accessible to students who have had an introductory quantum mechanics course. There is also considerable material for advanced researchers, and chapters in the book cover both methodology and applications. The book will be useful to students and researchers in physics, chemistry, applied math, and computational dynamics.

The centerpiece of the thesis is the search for muon neutrino to electron neutrino oscillations which would indicate a non-zero mixing angle between the first and third neutrino generations ( 13), currently the holy grail of neutrino physics. The optimal extraction of the electron neutrino oscillation signal is based on the novel library event matching (LEM) method which Ochoa developed and implemented together with colleagues at Caltech and at Cambridge, which improves MINOS (Main Injector Neutrino Oscillator Search) reach for establishing an oscillation signal over any other method. LEM will now be the basis for MINOS final results, and will likely keep MINOS at the forefront of this field until it completes its data taking in 2011. Ochoa and his colleagues also developed the successful plan to run MINOS with a beam tuned for antineutrinos, to make a sensitive test of CPT symmetry by comparing the inter-generational mass splitting for neutrinos and antineutrinos. Ochoa s in-depth, creative approach to the solution of a variety of complex experimental problems is an outstanding example for graduate students and longtime practitioners of experimental physics alike. Some of the most exciting results in this field to emerge in the near future may find their foundations in this thesis.

This book provides an overview of recent progress in computer simulations of nonperturbative phenomena in quantum field theory, particularly in the context of the lattice approach. It is a collection of extensive self-contained reviews of various subtopics, including algorithms, spectroscopy, finite temperature physics, Yukawa and chiral theories, bounds on the Higgs meson mass, the renormalization group, and weak decays of hadrons.Physicists with some knowledge of lattice gauge ideas will find this book a useful and interesting source of information on the recent developments in the field.

This book provides an overview of recent progress in computer simulations of nonperturbative phenomena in quantum field theory, particularly in the context of the lattice approach. It is a collection of extensive self-contained reviews of various subtopics, including algorithms, spectroscopy, finite temperature physics, Yukawa and chiral theories, bounds on the Higgs meson mass, the renormalization group, and weak decays of hadrons.Physicists with some knowledge of lattice gauge ideas will find this book a useful and interesting source of information on the recent developments in the field.

Recently, analogies between laboratory physics (e.g. quantum optics and condensed matter) and gravitational/cosmological phenomena such as black holes have attracted an increasing interest. This book contains a series of selected lectures devoted to this new and rapidly developing field. Various analogies connecting (apparently) different areas in physics are presented in order to bridge the gap between them and to provide an alternative point of view.

This book treats modern aspects of open systems, measurement, and decoherence in relativistic quantum theory. It starts with a comprehensive introduction to the problems related to measuring local and nonlocal observables and the constraints imposed by the causality principle. In the articles that follow, the emphasis lies on new theoretical models. Quantum dynamical semigroups and stochastic processes in Hilbert space are introduced, as are dynamical reduction models. Further topics include relativistic generalizations of the continuous spontaneous localization model and of the quantum state diffusion model and decoherence and the dynamical selection of preferred basis sets in the framework of continuous measurement theory and of the decoherent histories approach. Mathematical aspects of quantum measurement theory and dynamical entropies are also studied from the viewpoint of the operational approach to quantum mechanics.

Compiled to illustrate the recent history of Quantum Field Theory and its trends, this collection of selected reprints by Jurg Froehlich, a leading theoretician in the field, is a comprehensive guide of the more mathematical aspects of the subject. Results and methods of the past fifteen years are reviewed. The analytical methods employed are non-perturbative and, for the larger part, mathematically rigorous. Most articles are review articles surveying certain important developments in quantum field theory and guiding the reader towards the original literature.The volume begins with a comprehensive introduction by Jurg Froehlich.The theory of phase transitions and continuous symmetry breaking is reviewed in the first section. The second section discusses the non-perturbative quantization of topological solitons. The third section is devoted to the study of gauge fields. A paper on the triviality of 4 - theory in four and more dimensions is found in the fourth section, while the fifth contains two articles on "random geometry". The sixth and final part addresses topics in low-dimensional quantum field theory, including braid statistics, two-dimensional conformal field theory and an application to condensed matter theory.

The advent of new experimental techniques has made possible a new generation of more precise experimental tests of fundamental quantum mechanicsl. This workshop addressed the confrontation of new and proposed experimental tests of quantum mechanics with standard and nonstandard quantum theory. The broad, cross-disciplinary view of the subject brought together eminent theorists and experimentalists from diverse fields.

Grometstein explains modern physics with enthusiasm, wit and insight. As he presents the usual milestones in the history of modern physics, his central focus is the historical debate regarding the nature of light: is it a particle or is it a wave? This book will be read by generations of students in physical science who seek a well written discussion of these important issues. Grometstein includes material which is quite recent, thus making the present volume particularly useful.

How does the theoretical world of quantum physics create our everyday life?