Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.

1bis text is meant to be a view of the quantum mechanical fonnalism as it develops with the successive introduction of different types oftransfonnations. In particular, it is meant to help the readers with three tasks: acquainting themselves with a general and direct approach to the quantum mechanics of spin one-half and spin-one particles, primarily leptons, photons and massive vector bosons, and to some extent quarks; finding out what some of the related areas of current research interest are; and, last and foremost, trying to understand the subject, beginning with and stressing the principles involved. The exposition is based on finite-dimensional representations of the homogeneous Lorentz group, and the subsequent introduction of gauge transformations, of the Abelian and non Abelian varieties. Reference to classical mechanics is avoided. Acting on the simple basis spinors and vectors, Lorentz transfonnations generate wave and field functions. Equations are obtained by the relativistic generalization of the addition of angular momenta, the wave or field functions being the solutions. For zero mass the equations may be obtained as the limits of the equations for the massive cases or by the application of the Euclidian group in two dimensions. The latter approach is illuminating in that it uncovers a loss in generality resulting from the former. Identifying momenta as eigenvalues of translations demonstrates covariance under the inhomogeneous Lorentz or Poincare group. Various representations of wave and field functions are given."

This book is a new edition of Volumes 3 and 4 of Walter Thirring's famous textbook on mathematical physics. The first part is devoted to quantum mechanics and especially to its applications to scattering theory, atoms and molecules. The second part deals with quantum statistical mechanics examining fundamental concepts like entropy, ergodicity and thermodynamic functions. The author builds on an axiomatic basis and uses tools from functional analysis: bounded and unbounded operators on Hilbert space, operator algebras etc. Mathematics is shown to explain the axioms in depth and to provide the right tool for testing numerical data in experiments.

This volume presents a series of articles concerning current important topics in quantum chemistry.

On June 19th 1999, the European Ministers of Education signed the Bologna Dec laration, with which they agreed that the European university education should be uniformized throughout Europe and based on the two cycle bachelor master's sys tem. The Institute for Theoretical Physics at Utrecht University quickly responded to this new challenge and created an international master's programme in Theoret ical Physics which started running in the summer of 2000. At present, the master's programme is a so called prestige master at Utrecht University, and it aims at train ing motivated students to become sophisticated researchers in theoretical physics. The programme is built on the philosophy that modern theoretical physics is guided by universal principles that can be applied to any sub?eld of physics. As a result, the basis of the master's programme consists of the obligatory courses Statistical Field Theory and Quantum Field Theory. These focus in particular on the general concepts of quantum ?eld theory, rather than on the wide variety of possible applica tions. These applications are left to optional courses that build upon the ?rm concep tual basis given in the obligatory courses. The subjects of these optional courses in clude, for instance, Strongly Correlated Electrons, Spintronics, Bose Einstein Con densation, The Standard Model, Cosmology, and String Theory.

n Angular Momentum Theory for Diatomic Molecules, R R method of trees, 3 construct the wave functions of more complicated systems for ex- ple many electron atoms or molecules. However, it was soon realized that unless the continuum is included, a set of hydrogenlike orbitals is not complete. To remedy this defect, Shull and Lowdin [273] - troduced sets of radial functions which could be expressed in terms of Laguerre polynomials multiplied by exponential factors. The sets were constructed in such a way as to be complete, i. e. any radial fu- tion obeying the appropriate boundary conditions could be expanded in terms of the Shull-Lowdin basis sets. Later Rotenberg [256, 257] gave the name "Sturmian" to basis sets of this type in order to emp- size their connection with Sturm-Liouville theory. There is a large and rapidly-growing literature on Sturmian basis functions; and selections from this literature are cited in the bibliography. In 1968, Goscinski [138] completed a study ofthe properties ofSt- rnian basis sets, formulating the problem in such a way as to make generalization of the concept very easy. In the present text, we shall follow Goscinski's easily generalizable definition of Sturmians.

This thesis discusses in detail the measurement of the polarizations of all S-wave vector quarkonium states in LHC proton-proton collisions with the CMS detector. Heavy quarkonium states constitute an ideal laboratory to study non-perturbative effects of quantum chromodynamics and to understand how quarks bind into hadrons. The experimental results are interpreted through an original phenomenological approach, which leads to a coherent picture of quarkonium production cross sections and polarizations within a simple model, dominated by one single color-octet production mechanism. These findings provide new insights into the dynamics of heavy quarkonium production at the LHC, an important step towards a satisfactory understanding of hadron formation within the standard model of particle physics.

This thesis reports on experiments in which the motion of a mechanical oscillator is measured with unprecedented precision. The position fluctuations of the oscillator-a glass nanostring-are measured with an imprecision that is sufficient to resolve its quantum zero-point motion within its thermal decoherence time. The concomitant observation of measurement back-action, in accordance with Heisenberg's uncertainty principle, verifies the principles of linear quantum measurements on a macroscopic mechanical object. The record of the measurement is used to perform feedback control so as to suppress both classical thermal motion and quantum measurement back-action. These results verify some of the central and long-standing predictions of quantum measurement theory applied to a macroscopic object. The act of measurement not only perturbs the subject of the measurement-the mechanical oscillator-but also changes the state of the light used to make the measurement. This prediction is verified by demonstrating that the optical field, after having interacted with the mechanical oscillator, contains quantum correlations that render its quadrature fluctuations smaller than those of the vacuum - i.e., the light is squeezed. Lastly, the thesis reports on some of the first feedback control experiments involving macroscopic objects in the quantum regime, together with an exploration of the quantum limit of feedback control. The book offers a pedagogical account of linear measurement theory, its realization via optical interferometry, and contains a detailed guide to precision optical interferometry..

This subject is developed for readers with a fairly good knowledge of classical mechanics, electrodynamics and theory of relativity. The mathematics of linear vector spaces and matrices required is included as text and appendices. All principles and techniques are explained with illustrative applications. A Hilbert space formulation of the basic principles and the equations of motion are adopted at the outset. The treatment of linear vector spaces, matrices, angular momentum, relativistic wave equations, quantum field theory and the interpretational problem, is given in a more detailed way than in most books on quantum mechanics. Topics covered include Clebsch-Gordon and Racah coefficients, 9-j symbols and spherical tensors, the Klein-Gordon and the Weyl equations, Feynman's path-integral formalism, Feynman diagrams, Normal Products and Wick's Theorem, the EPR paradox, Hidden-variables theories and Bell's inequality. A number of problems are included with a view to supplementing the text. The present edition includes boundary value problems, representation theory, Fermi-Gas Model of the nuclei, Imaginary-mass Klein-Gordon equation, covariant and contravariant vectors, explanations of the EPR paradox and Einstein's concept of locality versus determinism.

Written by one of the founding fathers of Quantum Information, this book gives an accessible (albeit mathematically rigorous), self-contained introduction to quantum information theory. The central role is played by the concept of quantum channel and its entropic and information characteristics. In this revised edition, the main results have been updated to reflect the most recent developments in this very active field of research.

New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.

This thesis presents two production cross-section measurements of pairs of massive bosons using final states with leptons, made with the ATLAS detector at the Large Hadron Collider. The first measurement, performed using data collected in 2012 at center-of-mass energy s = 8 TeV, is the first fiducial and differential cross-section measurement of the production of the Higgs Boson when it decays to four charged leptons (electrons or muons). The second measurement is the first fiducial and inclusive production cross-section measurement of WZ pairs at center-of-mass energy s = 13 TeV using final states with three charged leptons. A significant portion of the thesis focuses on the methods used to identify electrons from massive boson decay-important for many flagship measurements-and on assessing the efficiency of these particle identification techniques. The chapter discussing the WZ pair cross-section measurement provides a detailed example of an estimate of lepton background in the context of an analysis with three leptons in the final state.

The first part of this third volume of Wigner's Collected Works is devoted to his analysis of symmetries in quantum mechanics, of the relativistic wave equations, of relativistic particle theory, and of field theory. It is introduced by the masterly annotation of Arthur S. Wightman. Abner Shimony annotates the second part where the reader will find Wigner's contributions to the foundations of quantum physics and to the problems of measurement.

This text builds a solid introduction to the concepts and techniques of quantum mechanics in settings where the phenomena treated are sufficiently simple that the student does not face two fundamental difficulties simultaneously: viz, that of learning quantum mechanics and that of learning how to assess the validity of models or the reliability of approximations. The treatment thus confines itself to systems that can either be solved exactly or be handled by well-controlled, plausible approximations. With few exceptions, this means systems with a small number of degrees of freedom. The exceptions are a first pass at many-electron atoms, the electromagnetic field, and the Dirac equation. (The inclusion of these last two topics reflects the now widely-held belief that every physicist should have at least a nodding acquaintance with these cornerstones of modern physics.) Born in Vienna, Kurt Gottfried emigrated to Canada in 1939 and received his Ph.D. in theoretical physics from MIT in 1955. He is professor of physics at Cornell University, and had previously been at Harvard University, the Massachusetts Institute of Technology, and at CERN in Geneva. He is the co-author of Concepts of Particle Physics (with V.F. Weisskopf), and of The Fallacy of Star Wars and Crisis, Stability, and Nuclear War. Gottfried has an active interest in arms control and human rights and is a founder and currently the Chair of the Union of Concerned Scientists.

In this monograph, we shall present a new mathematical formulation of quantum theory, clarify a number of discrepancies within the prior formulation of quantum theory, give new applications to experiments in physics, and extend the realm of application of quantum theory well beyond physics. Here, we motivate this new formulation and sketch how it developed. Since the publication of Dirac's famous book on quantum mechanics [Dirac, 1930] and von Neumann's classic text on the mathematical foundations of quantum mechanics two years later [von Neumann, 1932], there have appeared a number of lines of development, the intent of each being to enrich quantum theory by extra polating or even modifying the original basic structure. These lines of development have seemed to go in different directions, the major directions of which are identified here: First is the introduction of group theoretical methods [Weyl, 1928; Wigner, 1931] with the natural extension to coherent state theory [Klauder and Sudarshan, 1968; Peremolov, 1971]. The call for an axiomatic approach to physics [Hilbert, 1900; Sixth Problem] led to the development of quantum logic [Mackey, 1963; Jauch, 1968; Varadarajan, 1968, 1970; Piron, 1976; Beltrametti & Cassinelli, 1981], to the creation of the operational approach [Ludwig, 1983-85, 1985; Davies, 1976] with its application to quantum communication theory [Helstrom, 1976; Holevo, 1982), and to the development of the C* approach [Emch, 1972]. An approach through stochastic differential equations ("stochastic mechanics") was developed [Nelson, 1964, 1966, 1967].

In a distilled and pedagogical fashion, the contributions to this volume of the famous summer school in Les Houches cover the recent developments in supersymmetric string theory, the gauge theory/string theory correspondence and string duality. Further chapters deal with quantum gravity and D-brane geometry. Black hole mechanics and cosmology are treated too, as well as the AdS-CFT correspondence. The book is a comprehensive introduction to the recent developments in string/M-theory and quantum gravity. It addresses graduate students in physics and astrophysics.

This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schroedinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell's inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result. This book will be of interest to a wide readership seeking to understand modern quantum mechanics and its potential applications.

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.

The stochastic gravitational-wave background (SGWB) is by far the most difficult source of gravitational radiation detect. At the same time, it is the most interesting and intriguing one. This book describes the initial detection of the SGWB and describes the underlying mathematics behind one of the most amazing discoveries of the 21st century. On the experimental side it would mean that interferometric gravitational wave detectors work even better than expected. On the observational side, such a detection could give us information about the very early Universe, information that could not be obtained otherwise. Even negative results and improved upper bounds could put constraints on many cosmological and particle physics models.

Revue sur la theorie des D-modules et modeles d'operateurs pseudodifferentiells, A Survey on the Theory of D-modules. Models for Pseudodifferential Operators.- Fourier Transform and Differential Equations.- Excursions and Ito Calculus in Nelson's Stochastic Mechanics.- Stark-Wannier Resonant States.- Spectral Properties of Adiabatically Perturbed Differential Operators with the Periodic Coefficients.- Quantum Tunnelling for Bloch Electrons in Small Electric Fields.- Asymptotic Invariant Subspaces; Abiabatic Theorems and Block Diagonalisation.- On the Quantum Hall-Effect.- Magnetic Schroedinger Operators and Effective Hamiltonians.- Perturbations of Supersymmetric Systems in Quantum Mechanics.- On the Eigenvalues of a Perturbed Harmonic Oscillator.- On Topics in Spectral and Stochastic Analysis for Schroedinger Operators.- Asymptotic Observables in the N-Body Quantum Long Range Scattering.- Spectral Properties of Bent Quantum Wires.- Eigenfunction Expansions for Hyperbolic Laplacians.- The Method of Differential Inequalities.- Supersymmetric Quantum Mechanics.- Propagation des singularites GEVREY pour la diffraction.- Reduction and Geometric Prequantization at the Cotangent Level.- Dirac Particles in Magnetic Fields.- On the Quasi-Stationary Approach to Scattering for Perturbations Periodic in Time.- Existence, Uniqueness and Some Properties of Schroedinger Propagators.

This monograph is accessible to anyone with an undergraduate background in quantum mechanics, electromagnetism and some solid state physics. It describes in detail the properties of particles and fields in quasi-two-dimensional systems used to approximate realistic quantum heterostructures. Here the authors treat wires, i.e. they assume an infinite hardwall potential for the system. They discuss bound states, the properties of transmission and reflection, conductance, etc. It is shown that the simple models developed in this book in detail are capable of understanding even complex physical phenomena. The methods are applied to optical states in photonic crystals, and similarities and differences between those and electronic states in quantum heterostructures and electromagnetic fields in waveguides are discussed.

The present book takes the discovery that quantum-like behaviour is not solely reserved to atomic particles one step further. If electrons are modelled as vibrating droplets instead of the usually assumed point objects, and if the classical laws of nature are applied, then exactly the same behaviour as in quantum theory is found, quantitatively correct! The world of atoms is strange and quantum mechanics, the theory of this world, is almost magic. Or is it? Tiny droplets of oil bouncing round on a fluid surface can also mimic the world of quantum mechanics. For the layman - for whom the main part of this book is written - this is good news. If the everyday laws of nature can conspire to show up quantum-like phenomena, there is hope to form mental pictures how the atomic world works. The book is almost formula-free, and explains everything by using many sketches and diagrams. The mathematical derivations underlying the main text are kept separate in a -peer reviewed - appendix. The author, a retired professor of Flight Mechanics and Propulsion at the Delft University of Technology, chose to publish his findings in this mixed popular and scientific form, because he found that interested laymen more often than professional physicists feel the need to form visualisations of quantum phenomena.

In this thesis the author discusses the phenomenology of supersymmetric models by means of experimental data set analysis of the electric dipole moment. There is an evaluation of the elementary processes contributing to the electric dipole moments within R-parity-violating supersymmetry, which call for higher-order perturbative computations.

A new method based on linear programming is developed and for the first time the non-trivial parameter space of R-parity violation respecting the constraints from existing experimental data of the electric dipole moment is revealed. As well, the impressive efficiency of the new method in scanning the parameter space of the R-parity-violating sector is effectively demonstrated. This new method makes it possible to extract from the experimental data a more reliable constraint on the R-parity violation.

The problem of irreversibility is ubiquitous in physics and chemistry. The present book attempts to present a unified theoretical and conceptual framework for the description of various irreversible phenomena in quantum mechanics. In a sense, this book supplements conventional textbooks on quantum mechanics by including the theory of irreversibilities. However, the content and style of this book are more appropriate for a monograph than a textbook. We have tried to arrange the material so that, as far as possible, the reader need not continually refer elsewhere. The references to the literature make no pretense of completeness. The book is by no means a survey of present theoretical work. We have tried to highlight the basic principles and their results, while the attention has been mainly paid to the problems in which the author himself has been involved. The book as a whole is designed for the reader with knowledge of theoretical physics (especially quantum mechanics) at university level. This book is based on the courses of lectures given at the Chemistry Department of Tel-Aviv University.