This is a collection of papers on a variety of topics of current interest in mathematical physics: integrable systems, quantum groups, topological quantum theory, string theory. Some of the contributions are lengthy reviews of lasting value on subjects like symplectic geometry of the Chern-Simons theory or on mirror symmetry. The book addresses graduate students as well as researchers in mathematical physics.

The fifteenth European Conference on Few-Body Problems in Physics has taken place during the week of June 5th to 9th, in the lovely village of Peniscola, approximately midway between Barcelona and Valencia on the Mediterranean coast. This conference continues the tradition initiated in 1972 at Budapest, where the first conference took place, and followed in Graz (1973), Tiibingen (1975), Vlieland (1976), Uppsala (1977), Dubna (1979), Sesimbra (1980), Fer- rara (1981), Tbilisi (1984), Fontevraud (1987), Uzhgorod (1990), Elba (1991) and Amsterdam (1993). During this week, a total of one hundred and fifty one scientist were exchang- ing their knowledge and initiatives in this broad field of Few-Body Physics. Even if the name of the conference restricts its domain to Europe, there has been an important participation of scientists from non-European countries. A conference with more than twenty years of tradition is already an au- tonomous being, with a noticeable inertia. Nevertheless, it is a reasonable thought to bend this inertia trying to introduce some innovation, of course, without any damage to the basic structure and objectives of the conference.

This thesis explores the idea that the Higgs boson of the Standard Model and the cosmological inflation are just two manifestations of one and the same scalar field - the Higgs-inflation. By this unification two energy scales that are separated by many orders of magnitude are connected, thereby building a bridge between particle physics and cosmology. An essential ingredient for making this model consistent with observational data is a strong non-minimal coupling to gravity. Predictions for the value of the Higgs mass as well as for cosmological parameters are derived, and can be tested by future experiments. The results become especially exciting in the light of the recently announced discovery of the Higgs boson.
The model of non-minimal Higgs inflation is also used in a quantum cosmological context to predict initial conditions for inflation. These results can in turn be tested by the detection of primordial gravitational waves.
Thepresentation includesall introductory material about cosmology and the Standard Model that is essential forthe further understanding. It also provides an introduction to the mathematical methods used to calculate the effective action by heat kernel methods."

Written in a pedagogical way, the articles in this book address graduate students as well as researchers and are well suited for seminar work. Subjects at the forefront of nuclear research, bordering other areas of many-particle physics, such as electron scattering at different energy scales, new physics with radioactive beams, multifragmentation, relativistic nuclear physics, high spin nuclear problems, chaos, the role of the continuum in nuclear physics or recent calculations with the shell model are presented. It is felt that the topics treated in this book address the main future lines of development of nuclear physics.

The amazing accuracy in verifying quantum effects experimentally has recently renewed interest in quantum mechanical measurement theory. In this book the authors give within the Hilbert space formulation of quantum mechanics a systematic exposition of the quantum theory of measurement. Their approach includes the concepts of unsharp objectification and of nonunitary transformations needed for a unifying description of various detailed investigations. The book addresses advanced students and researchers in physics and philosophy of science. In this second edition Chaps. II-IV have been substantially rewritten. In particular, an insolubility theorem for the objectification problem has been formulated in full generality, which includes unsharp object observables as well as unsharp pointers.

This volume has its origin in the Semigroup Symposium which was organized in connection with the 21st International Colloquium on Group Theoretical Methods in Physics (ICGTMP) at Goslar, Germany, July 16-21, 1996. Just as groups are important tools for the description of reversible physical processes, semigroups are indispensable in the description of irreversible physical processes in which a direction of time is distinguished. There is ample evidence of time asymmetry in the microphysical world. The desire to go beyond the stationary systems has generated much recent effort and discussion regarding the application of semigroups to time-asymmetric processes. The book should be of interest to scientists and graduate students

The book covers the basics and some generalizations of Monte Carlo methods and its applications to discrete and field theoretic models. It covers the study of nonequilibrium models of granular media by computer simulation and pattern formation. Furthermore, the lectures deal with details of phenomena such as chaos, segregation, pattern formation and phase transitions, convection, fluidification, density waves, surface reaction and growth, spread of epidemics, acoustics, deformation, etc. The book addresses students in physics and scientific computation. It should be a valuable reference work for researchers as well.

In this thesis, novel Monte Carlo methods for precisely calculating the critical phenomena of the effectively frustrated quantum spin system are developed and applied to the critical phenomena of the spin-Peierls systems. Three significant methods are introduced for the first time: a new optimization algorithm of the Markov chain transition kernel based on the geometric weight-allocation approach, the extension of the worm (directed-loop) algorithm to nonconserved particles, and the combination with the level spectroscopy. Utilizing these methods, the phase diagram of the one-dimensional XXZ spin-Peierls system is elucidated. Furthermore, the multi-chain and two-dimensional spin-Peierls systems with interchain lattice interaction are investigated. The unbiased simulation shows that the interesting quantum phase transition between the 1D-like liquid phase and the macroscopically-degenerated dimer phase occurs on the fully-frustrated parameter line that separates the doubly-degenerated dimer phases in the two-dimensional phase diagram. The spin-phonon interaction in the spin-Peierls system introduces the spin frustration, which usually hinders the quantum Monte Carlo analysis, owing to the notorious negative sign problem. In this thesis, the author has succeeded in precisely calculating the critical phenomena of the effectively frustrated quantum spin system by means of the quantum Monte Carlo method without the negative sign.

In this volume seven leading theoreticians and experimenters review the origin of the asymmetry of matter and antimatter in the Big Bang, solar neutrinos, the physics of enormous densities and temperatures in stars and of immense magnetic fields around collapsed stars, strong electric fields in heavy ion collisions, and the extreme conditions in quark-gluon plasmas. The articles address nuclear and particle physicists, especially graduate students, but also astrophysicists and cosmologists, since they have to deal with events under the extreme physical conditions discussed here.

Several of the very foundations of the cosmological standard model the baryon asymmetry of the universe, dark matter, and the origin of the hot big bang itself still call for an explanation from the perspective of fundamental physics. This workadvocates one intriguing possibility for a consistent cosmology that fills in the theoretical gaps while being fully in accordance with the observational data. At very high energies, the universe might have been in a false vacuum state that preserved B-L, the difference between the baryon number B and the lepton number L as a local symmetry. In this state, the universe experienced a stage of hybrid inflation that only ended when the false vacuum became unstable and decayed, in the course of a waterfall transition, into a phase with spontaneously broken B-L symmetry. This B-L Phase Transition was accompanied by tachyonic preheating that transferred almost the entire energy of the false vacuum into a gas of B-L Higgs bosons, which in turn decayed into heavy Majorana neutrinos. Eventually, these neutrinos decayed into massless radiation, thereby producing the entropy of the hot big bang, generating the baryon asymmetry of the universe via the leptogenesis mechanism and setting the stage for the production of dark matter. Next to a variety of conceptual novelties and phenomenological predictions, the main achievement of the thesis is hence the fascinating notion that the leading role in the first act of our universe might have actually been played by neutrinos.
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A modern Hamiltonian theory offering a unified treatment of all types of systems (i.e. finite, lattice, and field) is presented. Particular attention is paid to nonlinear systems that have more than one Hamiltonian formulation in a single coordinate system. As this property is closely related to integrability, this book presents an algebraic theory of integrable systems. The book is intended for scientists, lecturers, and students interested in the field.

Special relativity and quantum mechanics are likely to remain the two most important languages in physics for many years to come. The underlying language for both disciplines is group theory. Eugene P. Wigner's 1939 paper on the Unitary Representations of the Inhomogeneous Lorentz Group laid the foundation for unifying the concepts and algorithms of quantum mechanics and special relativity. In view of the strong current interest in the space-time symmetries of elementary particles, it is safe to say that Wigner's 1939 paper was fifty years ahead of its time. This edited volume consists of Wigner's 1939 paper and the major papers on the Lorentz group published since 1939. . This volume is intended for graduate and advanced undergraduate students in physics and mathematics, as well as mature physicists wishing to understand the more fundamental aspects of physics than are available from the fashion-oriented theoretical models which come and go. The original papers contained in this volume are useful as supplementary reading material for students in courses on group theory, relativistic quantum mechanics and quantum field theory, relativistic electrodynamics, general relativity, and elementary particle physics. This reprint collection is an extension of the textbook by the present editors entitled "Theory and Applications of the Poincare Group." Since this book is largely based on the articles contained herein, the present volume should be viewed as a reading for the previous work. continuation of and supplementary We would like to thank Professors J. Bjorken, R. Feynman, R. Hofstadter, J.

The articles collected in this volume cover topics ranging from Planck-scale physics to galaxy clustering. They deal with various new ideas from cosmology, astrophysics and particle physics that might lead to a better understanding of our physical universe. Among the topics covered are inflationary models, nucleosynthesis, dark matter, large-scale clustering, cosmic microwave background radiations and more. The book addresses researchers but it also gives a good overview of the subject for graduate students in astrophysics and particle physics.

The idea of this book originated from two series of lectures given by us at the Physics Department of the Catholic University of Petr6polis, in Brazil. Its aim is to present an introduction to the "algebraic" method in the perturbative renormalization of relativistic quantum field theory. Although this approach goes back to the pioneering works of Symanzik in the early 1970s and was systematized by Becchi, Rouet and Stora as early as 1972-1974, its full value has not yet been widely appreciated by the practitioners of quantum field theory. Becchi, Rouet and Stora have, however, shown it to be a powerful tool for proving the renormalizability of theories with (broken) symmetries and of gauge theories. We have thus found it pertinent to collect in a self-contained manner the available information on algebraic renormalization, which was previously scattered in many original papers and in a few older review articles. Although we have taken care to adapt the level of this book to that of a po- graduate (Ph. D. ) course, more advanced researchers will also certainly find it useful. The deeper knowledge of renormalization theory we hope readers will acquire should help them to face the difficult problems of quantum field theory. It should also be very helpful to the more phenomenology oriented readers who want to famili- ize themselves with the formalism of renormalization theory, a necessity in view of the sophisticated perturbative calculations currently being done, in particular in the standard model of particle interactions.

In this volume, experimentalists and theoreticians discuss which experiments and calculations are needed to make significant progress in the field and also how experiments and theoretical descriptions can be compared. The topics treated are the electromagnetic production of Goldstone bosons, pion--pion and pion--nucleon interactions, hadron polarizability and form factors.

In this book the concept of indistinguishability is defined for identical particles by the symmetry of the state. It applies, therefore, to both the classical and the quantum framework. The author describes symmetric statistical operators and classifies these by means of extreme points. For the description of infinitely extendible interchangeable random variables de Finetti's theorem is derived and generalizations covering the Poisson limit and the central limit are presented. A characterization and interpretation of the integral representations of classical photon states in quantum optics are derived in abelian subalgebras. Unextendible indistinguishable particles are analyzed in the context of nonclassical photon states. The book addresses mathematical physicists and philosophers of science.

The book contains the notes of the lectures presented by outstanding experts at the 7th EADN School on plasma astrophysics. It is an up-to-date review of a number of basic topics in the physics of cosmic plasmas. The subject is treated both from a theoretical point of view and from that of the observational and diagnostic tools that provide us with the physically relevant data. The reader will have at hands a comprehensive and rather complete presentation of the subject, thanks also to the parallel development of the theoretical and experimental aspects. The book addresses graduate students and researchers in different areas who want to have a rapid and up-to-date introduction to this subject.

Like relativity and quantum theory chaos research is another prominent concept of 20th century physics that has triggered deep and far-reaching discussions in the philosophy of science. In this volume outstanding scientists discuss the fundamental problems of the concepts of law and of prediction. They present their views in their contributions to this volume, but they also are exposed to criticism in transcriptions of recordings made during discussions and in comments on their views also published in this book. Although all authors assume familiarity with some background in physics they also address the philosophers of science and even a general audience interested in modern science's contribution to a deeper understanding of reality.

The Handbook of Feynman Path Integrals appears just fifty years after Richard Feynman published his pioneering paper in 1948 entitled "Space-Time Approach to Non-Relativistic Quantum Mechanics", in which he introduced his new formulation of quantum mechanics in terms of path integrals. The book presents for the first time a comprehensive table of Feynman path integrals together with an extensive list of references; it will serve the reader as a thorough introduction to the theory of path integrals. As a reference book, it is unique in its scope and will be essential for many physicists, chemists and mathematicians working in different areas of research.

Small-scale structures in turbulent flows appear as a subtle mixture of order and chaos that could play an important role in the energetics. The aim here is a better understanding of the similarities and differences between vortex and current dynamics, and of the influence of these structures on the statistical and transport properties of hydrodynamic and magnetohydrodynamic turbulence, with special concern for fusion plasmas, and solar or magnetospheric environments. Special emphasis is given to the intermittency at inertial scales and to the coherent structures at small scales. Magnetic reconnection and the dynamo effect are also discussed, together with the effect of stratification and inhomogeneity. The impact of hydrodynamic concepts on astro and geophysical observations are reviewed.

We consider quantum dynamical systems (in general, these could be either Hamiltonian or dissipative, but in this review we shall be interested only in quantum Hamiltonian systems) that have, at least formally, a classical limit. This means, in particular, that each time-dependent quantum-mechanical expectation value X (t) has as i cl Ii -+ 0 a limit Xi(t) -+ x1 )(t) of the corresponding classical sys- tem. Quantum-mechanical considerations include an additional di- mensionless parameter f = iiiconst. connected with the Planck constant Ii. Even in the quasiclassical region where f~ 1, the dy- namics of the quantum and classicalfunctions Xi(t) and XiCcl)(t) will be different, in general, and quantum dynamics for expectation val- ues may coincide with classical dynamics only for some finite time. This characteristic time-scale, TIi., could depend on several factors which will be discussed below, including: choice of expectation val- ues, initial state, physical parameters and so on. Thus, the problem arises in this connection: How to estimate the characteristic time- scale TIi. of the validity of the quasiclassical approximation and how to measure it in an experiment? For rather simple integrable quan- tum systems in the stable regions of motion of their corresponding classical phase space, this time-scale T" usually is of order (see, for example, [2]) const TIi. = p,li , (1.1) Q where p, is the dimensionless parameter of nonlinearity (discussed below) and a is a constant of the order of unity.

Volume 1 of the 5-volume Quantum Nanochemistry series presents an overall perspective of nuclear, atomic, molecular, and solids structures, and the observability and quantum properties as based on the quantum principles in their various levels of applications, from Planck, Bohr, Einstein, Schroedinger, Hartree-Fock, up to Feynman Path Integral approaches. The volume presents in a balanced manner the fundamental and advanced concepts, principles, and models as well as their first and novel combinations and applications in modeling complex natural or designed phenomena.

This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherent states, wavelets, and some of their generalizations, it emphasizes mathematical principles, subsuming the theories of both wavelets and coherent states into a single analytic structure. The approach allows the user to take a classical-like view of quantum states in physics.

Starting from the standard theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are square integrable over a homogeneous space; a further step allows one to dispense with the group context altogether. In this context, wavelets can be generated from coherent states of the affine group of the real line, and higher-dimensional wavelets arise from coherent states of other groups. The unified background makes transparent an entire range of properties of wavelets and coherent states. Many concrete examples, such as coherent states from semisimple Lie groups, Gazeau-Klauder coherent states, coherent states forthe relativity groups, and several kinds of wavelets, are discussed in detail. The book concludes with a palette of potentialapplications, from the quantum physically oriented, likethe quantum-classical transition or the construction of adequate states in quantum information, to the most innovative techniques to be used in data processing.

Intended as an introduction to current research for graduate students and others entering the field, the mathematical discussion is self-contained. With its extensive references to the research literature, the first edition of the book is already a proven compendium for physicists and mathematicians active in the field, and with full coverage of the latest theory and results the revised second edition is even more valuable."

This thesis describes a high-quality, high-precision method for the data analysis of an interesting elementary particle reaction. The data was collected at the Japanese B-meson factory KEKB with the Belle detector, one of the most successful large-scale experiments worldwide. CP violation is a subtle quantum effect that makes the world look different when simultaneously left and right and matter and antimatter are exchanged. This being a prerequisite for our own world to have developed from the big bang, there are only a few experimental indications of such effects, and their detection requires very intricate techniques. The discovery of CP violation in B meson decays garnered Kobayashi and Maskawa, who had predicted these findings as early as 1973, the 2008 Nobel prize in physics. This thesis describes in great detail what are by far the best measurements of branching ratios and CP violation parameters in two special reactions with two charm mesons in the final state. It presents an in-depth but accessible overview of the theory, phenomenology, experimental setup, data collection, Monte Carlo simulations, (blind) statistical data analysis, and systematic uncertainty studies.

Scattering amplitudes are fundamental and rich observables in quantum field theory. Based on the observation that, for massless particles of spin-one or more, scattering amplitudes are much simpler than expected from traditional Feynman diagram techniques, the broad aim of this work is to understand and exploit this hidden structure. It uses methods from twistor theory to provide new insights into the correspondence between scattering amplitudes in supersymmetric Yang-Mills theory and null polygonal Wilson loops. By additionally exploiting the symmetries of the problem, the author succeeds in developing new ways of computing scattering amplitudes.