World Scientific Lecture Notes In Physics – serie

This book provides a thorough discussion of the concepts and main consequences of special relativity. Treated in detail are the Lorentz transformations, their kinematical consequences (the so-called paradoxes), relativistic mechanics, electrodynamics as an example of a relativistic field theory, and the principal features of relativistic hydrodynamics. The book offers a logical development of special relativity from Einstein's principle of relativity alone; arrives at the essential statements of the theory by a direct approach — this emphasis is different from that of most books; and offers a concise introduction to tensor calculus as needed in special relativity. A selection of problems and documentation of the experimental tests of special relativity are given.

This book provides a thorough discussion of the concepts and main consequences of special relativity. Treated in detail are the Lorentz transformations, their kinematical consequences (the so-called paradoxes), relativistic mechanics, electrodynamics as an example of a relativistic field theory, and the principal features of relativistic hydrodynamics. The book offers a logical development of special relativity from Einstein's principle of relativity alone; arrives at the essential statements of the theory by a direct approach — this emphasis is different from that of most books; and offers a concise introduction to tensor calculus as needed in special relativity. A selection of problems and documentation of the experimental tests of special relativity are given.

These lecture notes deal with the problem of collective coordinates in many-body systems, which are treated as gauge systems in (0+1) dimensions. The resulting classical Dirac brackets are discussed, as well as the structure of the quantal space of wavefunctions. Emphasis is made on the application of the BRST formalism. Several systems displaying an approximate breakdown of symmetries are treated. Many-body physicists may find attractive both a rigorous formulation of the problem of collective coordinates and being introduced to the BRST formalism, which has become a fundamental tool in gauge theories. Field-theorists may find illuminating the applications to simpler mechanical examples. The notes are self-contained. In particular, they do not require a previous knowledge of either the BRST formalism or of collective transformations.

These lecture notes deal with the problem of collective coordinates in many-body systems, which are treated as gauge systems in (0+1) dimensions. The resulting classical Dirac brackets are discussed, as well as the structure of the quantal space of wavefunctions. Emphasis is made on the application of the BRST formalism. Several systems displaying an approximate breakdown of symmetries are treated. Many-body physicists may find attractive both a rigorous formulation of the problem of collective coordinates and being introduced to the BRST formalism, which has become a fundamental tool in gauge theories. Field-theorists may find illuminating the applications to simpler mechanical examples. The notes are self-contained. In particular, they do not require a previous knowledge of either the BRST formalism or of collective transformations.

The first half of the book presents the effective field approach, which is certainly the simplest approach to investigate cooperative phenomena and the accompanying phase transitions. It provides a common, intuitive approximation to the physics of such diverse phenomena as liquid-vapor transitions, ferromagnetism, superconductivity, order-disorder in alloys, ferroelectricity, superfluidity and ferroelasticity. The connection between the effective field approach and Landau's phenomenological theory is stressed. The latter half is devoted to some specific applications of the effective field concept to ferroelectric systems.

The first half of the book presents the effective field approach, which is certainly the simplest approach to investigate cooperative phenomena and the accompanying phase transitions. It provides a common, intuitive approximation to the physics of such diverse phenomena as liquid-vapor transitions, ferromagnetism, superconductivity, order-disorder in alloys, ferroelectricity, superfluidity and ferroelasticity. The connection between the effective field approach and Landau's phenomenological theory is stressed. The latter half is devoted to some specific applications of the effective field concept to ferroelectric systems.

Several different models have recently been proposed to explain High Temperature Superconductivity. This book gives an authoritative and up-to-date review of two such proposals, namely the Hubbard and Anyon Models. This invaluable reference is a must for all physicists interested in the fast-paced revolutionary field of High Temperature Superconductivity.

Several different models have recently been proposed to explain High Temperature Superconductivity. This book gives an authoritative and up-to-date review of two such proposals, namely the Hubbard and Anyon Models. This invaluable reference is a must for all physicists interested in the fast-paced revolutionary field of High Temperature Superconductivity.

This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrödinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects.

This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrödinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects.

Are neutrinos massless particles as predicted by the standard model of electroweak interactions? There are however many reasons to suspect that neutrinos may indeed be massive and understanding the neutrino mass may hold the key to our understanding of physics beyond the standard model.This book provides a comprehensive overview of our present understanding of neutrino mass in unified gauge theories, its phenomenological and cosmological implications. It is divided into four parts. The first part presents a model independent discussion of the properties of the neutrino and nature of the neutrino masses. Part 2 deals with neutrino masses in unified and grand unified theories. In Part 3, phenomenological implications of neutrino mass is discussed. This includes neutrino oscillations, neutrinoless double beta decay and electromagnetic properties of neutrinos. Part 4 considers the solar neutrino puzzle, SN1987A and cosmological constraints on the neutrino properties. The book is meant for beginning and advanced graduate students in particle physics as well as active researchers in the field. It contains an extensive list of references to the original literature.

Are neutrinos massless particles as predicted by the standard model of electroweak interactions? There are however many reasons to suspect that neutrinos may indeed be massive and understanding the neutrino mass may hold the key to our understanding of physics beyond the standard model.This book provides a comprehensive overview of our present understanding of neutrino mass in unified gauge theories, its phenomenological and cosmological implications. It is divided into four parts. The first part presents a model independent discussion of the properties of the neutrino and nature of the neutrino masses. Part 2 deals with neutrino masses in unified and grand unified theories. In Part 3, phenomenological implications of neutrino mass is discussed. This includes neutrino oscillations, neutrinoless double beta decay and electromagnetic properties of neutrinos. Part 4 considers the solar neutrino puzzle, SN1987A and cosmological constraints on the neutrino properties. The book is meant for beginning and advanced graduate students in particle physics as well as active researchers in the field. It contains an extensive list of references to the original literature.

This volume brings together a collection of review talks and popular science papers by the distinguished Soviet theorist Lev Okun. The talks were given at major international conferences on elementary particle physics during the 1980's. The papers discuss experimental tests of fundamental physical principles and the concept of mass in relativity theory.

This volume brings together a collection of review talks and popular science papers by the distinguished Soviet theorist Lev Okun. The talks were given at major international conferences on elementary particle physics during the 1980's. The papers discuss experimental tests of fundamental physical principles and the concept of mass in relativity theory.

In this book, distributions are introduced via sequences of functions. This approach due to Temple has two virtues:The Fourier transform is defined for functions and generalized to distributions, while the Green function is defined as the outstanding application of distributions. Using Fourier transforms, the Green functions of the important linear differential equations in physics are computed. Linear algebra is reviewed with emphasis on Hilbert spaces. The author explains how linear differential operators and Fourier transforms naturally fit into this frame, a point of view that leads straight to generalized fourier transforms and systems of special functions like spherical harmonics, Hermite, Laguerre, and Bessel functions.

This book introduces a large number of topics in lattice gauge theories, including analytical as well as numerical methods. It provides young physicists with the theoretical background and basic computational tools in order to be able to follow the extensive literature on the subject, and to carry out research on their own. Whenever possible, the basic ideas and technical inputs are demonstrated in simple examples, so as to avoid diverting the readers' attention from the main line of thought. Sufficient technical details are however given so that he can fill in the remaining details with the help of the cited literature without too much effort.This volume is designed for graduate students in theoretical elementary particle physics or statistical mechanics with a basic knowledge in Quantum Field Theory.

This book introduces a large number of topics in lattice gauge theories, including analytical as well as numerical methods. It provides young physicists with the theoretical background and basic computational tools in order to be able to follow the extensive literature on the subject, and to carry out research on their own. Whenever possible, the basic ideas and technical inputs are demonstrated in simple examples, so as to avoid diverting the readers' attention from the main line of thought. Sufficient technical details are however given so that he can fill in the remaining details with the help of the cited literature without too much effort.This volume is designed for graduate students in theoretical elementary particle physics or statistical mechanics with a basic knowledge in Quantum Field Theory.

The interest in membranes and higher dimensional extended geometrical objects was inspired by the great successes of the string and superstring, first in 1968-73 as a theory of hadrons and then since 1984 as a “theory of everything” — a unified theory of all interactions, including quantum gravity. In particular, membranes, “supermembranes” and “spinning membranes” have been studied since 1985; an unexpected connection with supergravity opened in 1988 some new prospects for a quantized theory. General theorems about higher dimensional “p-branes” or “extendons” were also derived. The subject is very promising, whether as a more comprehensive fundamental unification or as a description of composite hadrons.Where there are now probably some fifty texts of all kinds dealing with strings, this is the first treatise on membranes and higher dimensional extendons.

The interest in membranes and higher dimensional extended geometrical objects was inspired by the great successes of the string and superstring, first in 1968-73 as a theory of hadrons and then since 1984 as a “theory of everything” — a unified theory of all interactions, including quantum gravity. In particular, membranes, “supermembranes” and “spinning membranes” have been studied since 1985; an unexpected connection with supergravity opened in 1988 some new prospects for a quantized theory. General theorems about higher dimensional “p-branes” or “extendons” were also derived. The subject is very promising, whether as a more comprehensive fundamental unification or as a description of composite hadrons.Where there are now probably some fifty texts of all kinds dealing with strings, this is the first treatise on membranes and higher dimensional extendons.

In this book the author has tried to apply “a little imagination and thinking” to modelling dynamical phenomena from a classical atomic and molecular point of view. Nonlinearity is emphasized, as are phenomena which are elusive from the continuum mechanics point of view. FORTRAN programs are provided in the Appendices.

Understanding the quark structure of matter has been one of the most important advances in contemporary physics. It has unravelled a new and deeper level of structure in matter, and physics at that level reveals a unity and aesthetic simplicity never before attained. All forces emerge from a unique invariance principle and each of the basic interactions results from a specific symmetry property. Quarks interact among themselves through their “colour”, as now accurately described by quantum chromodynamics.This volume brings together eight major review articles by Maurice Jacob, a physicist at the forefront of research on the quark structure of matter. He has, in particular, been involved with two research topics in this field. The first is the study of hadronic jets, which one actually sees instead of quarks, because of the opacity of the vacuum to colour. The second is the search for quark matter, a new form of matter believed to exist at high temperatures, when the vacuum should become transparent to colour.The papers in this volume provide a comprehensive review of these phenomenological studies on the quark structure of matter, and also a fasinating insight into the pace of recent progress in these areas. The book comes complete with an original introduction by the author, and also contains a pedagogical review on what is a most engrossing and rewarding field of research in physics.

This volume is a collection of lectures and selected papers by Giorgio Parisi on the subjects of Field Theory (perturbative expansions, nonperturbative phenomena and phase transitions), Disordered Systems (mainly spin glasses) and Computer Simulations (lattice gauge theories).The basic problems discussed in the Field Theory section concern the interplay between perturbation theory and nonperturbative phenomena which are present when one deals with infrared or ultraviolet divergences or with nonconvergent perturbative expansions. The section on Disordered Systems contains a complete discussion about the replica method and its probabilistic interpretation, and also includes a short paper on multifractals. In the Simulations section, there is a series of lectures devoted to the study of quantum chromodynamics and a review paper on simulations in complex systems.The works of Giorgio Parisi have repeatedly displayed a remarkable depth of originality and innovation, and have paved the way for new research in many areas. This personal selection of his lectures and papers, complete with an original introduction by him, undoubtedly serves as a vital reference book for physicists and mathematicians working in these fields.

This is a text on classical general relativity from a geometrical viewpoint. Introductory chapters are provided on algebra, topology and manifold theory, together with a chapter on the basic ideas of space-time manifolds and Einstein's theory. There is a detailed account of algebraic structures and tensor classification in general relativity and also of the relationships between the metric, connection and curvature structures on space-times. The latter includes chapters on holonomy and sectional curvature. An extensive study is presented of symmetries in general relativity, including isometries, homotheties, conformal symmetries and affine, projective and curvature collineations. Several general properties of such symmetries are studied and a preparatory section on transformation groups and on the properties of Lie algebras of vector fields on manifolds is provided.

Gauge theory, which underlies modern particle physics as well as the theory of gravity, and hence all of physics as we know it today, is itself based on a few fundamental concepts, the consequences of which are often as beautiful as they are deep. Unfortunately, in view of the pressure to cover aspects of the theory that are necessary for its many important applications, very little space is usually devoted in textbooks and graduate courses to the treatment of these concepts. The present small volume is an attempt to help in some degree to redress this imbalance in the literature.The topics covered are elementary in the sense of being basic, not in the sense of being shallow or easy. Although all will already feature at the classical field level, and most even before the introduction of an action principle, they often lead one to pose some quite profound questions, so that much of the material treated is by necessity at the front line of research. The approach adopted is physically motivated, although there is no hesitation in introducing mathematical concepts when they are a help to understanding. In the presentation, little is assumed of the reader, and no pains has been spared to make the whole volume understandable to researchers in other fields and to graduate students, provided that the reader is willing to devote sufficient effort required by the subject matter. On the other hand, neither has there been any conscious attempt to avoid essential difficulties, or to trivialise concepts which are intrinsically abstruse. It is thus hoped that the result will be enjoyable reading for researchers and students alike.

Gauge theory, which underlies modern particle physics as well as the theory of gravity, and hence all of physics as we know it today, is itself based on a few fundamental concepts, the consequences of which are often as beautiful as they are deep. Unfortunately, in view of the pressure to cover aspects of the theory that are necessary for its many important applications, very little space is usually devoted in textbooks and graduate courses to the treatment of these concepts. The present small volume is an attempt to help in some degree to redress this imbalance in the literature.The topics covered are elementary in the sense of being basic, not in the sense of being shallow or easy. Although all will already feature at the classical field level, and most even before the introduction of an action principle, they often lead one to pose some quite profound questions, so that much of the material treated is by necessity at the front line of research. The approach adopted is physically motivated, although there is no hesitation in introducing mathematical concepts when they are a help to understanding. In the presentation, little is assumed of the reader, and no pains has been spared to make the whole volume understandable to researchers in other fields and to graduate students, provided that the reader is willing to devote sufficient effort required by the subject matter. On the other hand, neither has there been any conscious attempt to avoid essential difficulties, or to trivialise concepts which are intrinsically abstruse. It is thus hoped that the result will be enjoyable reading for researchers and students alike.

This book provides a readable account of the foundations of QFT, in particular of the Euclidean formulation with emphasis on the interplay between physical requirements and mathematical structures. The general structures underlying the conventional local (renormalizable) formulation of gauge QFT are discussed also on the basis of simple models. The mechanism of confinement, non-trivial topology and θ-vacua, chiral symmetry breaking and solution of the U(1) problem are clarified through a careful analysis of the Schwinger model, which settles unclear or debated points.

This book provides a readable account of the foundations of QFT, in particular of the Euclidean formulation with emphasis on the interplay between physical requirements and mathematical structures. The general structures underlying the conventional local (renormalizable) formulation of gauge QFT are discussed also on the basis of simple models. The mechanism of confinement, non-trivial topology and θ-vacua, chiral symmetry breaking and solution of the U(1) problem are clarified through a careful analysis of the Schwinger model, which settles unclear or debated points.

These lectures are concerned with the application of high temperature superconductors to both passive and active high-frequency devices.The central issue addressed is the electrodynamics of granular superconductors, particularly where grain boundaries (either natural or synthetic) act as Josephson weak-links. Grain boundaries are responsible for residual dissipation and for unwanted dependence of the electromagnetic properties on ambient magnetic fields and on elevated power level. Properly controlled, similar weak-links are the key to high sensitivity dc and rf SQUIDS at readily accessible temperatures, and to modulators, mixers and detectors. Such structures may conveniently lead to superconductive electronic devices as well as coherent sources of radiation in the very far infrared.

These lectures are concerned with the application of high temperature superconductors to both passive and active high-frequency devices.The central issue addressed is the electrodynamics of granular superconductors, particularly where grain boundaries (either natural or synthetic) act as Josephson weak-links. Grain boundaries are responsible for residual dissipation and for unwanted dependence of the electromagnetic properties on ambient magnetic fields and on elevated power level. Properly controlled, similar weak-links are the key to high sensitivity dc and rf SQUIDS at readily accessible temperatures, and to modulators, mixers and detectors. Such structures may conveniently lead to superconductive electronic devices as well as coherent sources of radiation in the very far infrared.