A sequel to the well received book, Quantum Mechanics by T Y Wu, this book carries on where the earlier volume ends. This present volume follows the generally pedagogic style of Quantum Mechanics. The scope ranges from relativistic quantum mechanics to an introduction to quantum field theory with quantum electrodynamics as the basic example and ends with an exposition of important issues related to the standard model. The book presents the subject in basic and easy-to-grasp notions which will enhance the purpose of this book as a useful textbook in the area of relativistic quantum mechanics and quantum electrodynamics.

An introduction and comprehensive survey of the main issues in mesosocopic physics. Topics covered include quantum Hall effects, transport through quantum wires and dots, coherence in mesoscopic systems, spintronics, disordered systems, and solid state quantum computation. Some contributions are dedicated to the connections between nanoscience and biophysics and quantum optics.
Although the topics mentioned have many aspects in common, they span a wide area of physics. It is therefore especially important to provide a broad view of this rapidly expanding field. Thanks to the excellent presentations, the book will be found suitable both for young researchers who want to enter the field and stimulating for more experienced scientists.

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.

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.

Gravity, a Geometrical Course presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes.

Volume Two is covers black holes, cosmology and an introduction to supergravity. The aim of this volume is two-fold. It completes the presentation of GR and it introduces the reader to theory of gravitation beyond GR, which is supergravity. Starting with a short history of the black hole concept, the book covers the Kruskal extension of the Schwarzschild metric, the causal structures of Lorentzian manifolds, Penrose diagrams and a detailed analysis of the Kerr-Newman metric. An extensive historical account of the development of modern cosmology is followed by a detailed presentation of its mathematical structure, including non-isotropic cosmologies and billiards, de Sitter space and inflationary scenarios, perturbation theory and anisotropies of the Cosmic Microwave Background. The last three chapters deal with the mathematical and conceptual foundations of supergravity in the frame of free differential algebras. Branes are presented both as classical solutions of the bulk theory and as world-volume gauge theories with particular emphasis on the geometrical interpretation of kappa-supersymmetry. The rich bestiary of special geometries underlying supergravity lagrangians is presented, followed by a chapter providing glances on the equally rich collection of special solutions of supergravity.

Pietro Fre is Professor of Theoretical Physics at the University of Torino, Italy and is currently serving as Scientific Counsellor of the Italian Embassy in Moscow. His scientific passion lies in supergravity and all allied topics, since the inception of the field, in 1976. He was professor at SISSA, worked in the USA and at CERN. He has taught General Relativity for 15 years. He has previously two scientific monographs, Supergravity and Superstrings and The N=2 Wonderland, He is also the author of a popular science book on cosmology and two novels, in Italian."

The focus of the present work is nonrelativistic and relativistic quantum mechanics with standard applications to the hydrogen atom. The author has aimed at presenting quantum mechanics in a comprehensive yet accessible for mathematicians and other non-physicists. The genesis of quantum mechanics, its applications to basic quantum phenomena, and detailed explanations of the corresponding mathematical methods are presented. The exposition is formalized (whenever possible) on the basis of the coupled Schroedinger, Dirac and Maxwell equations. Aimed at upper graduate and graduate students in mathematical and physical science studies.

A definitive historical study of this scientific work and the human struggles that accompanied it from the very beginning. Drawing on such materials as the resources of the Archives for the History of Quantum Physics, the Niels Bohr Archives, and the archives and scientific correspondence of the principal quantum physicists, as well as Jagdish Mehras personal discussions over many years with most of the architects of quantum theory, the authors have written a rigorous scientific history in a deeply human context. This multivolume work presents a rich account of an intellectual triumph: a unique analysis of the creative scientific process, wrapped in the story of a great human enterprise. Its lessons will be an aid to those working in the sciences and humanities alike.

This thesis demonstrates a full Mach-Zehnder interferometer with interacting Bose-Einstein condensates confined on an atom chip. It relies on the coherent manipulation of atoms trapped in a magnetic double-well potential, for which the author developed a novel type of beam splitter. Particle-wave duality enables the construction of interferometers for matter waves, which complement optical interferometers in precision measurement devices, both for technological applications and fundamental tests. This requires the development of atom-optics analogues to beam splitters, phase shifters and recombiners. Particle interactions in the Bose-Einstein condensate lead to a nonlinearity, absent in photon optics. This is exploited to generate a non-classical state with reduced atom-number fluctuations inside the interferometer. This state is then used to study the interaction-induced dephasing of the quantum superposition. The resulting coherence times are found to be a factor of three longer than expected for coherent states, highlighting the potential of entanglement as a resource for quantum-enhanced metrology.

This monograph, unique in the literature, is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing. Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Among the lensing topics discussed are multiple quasars, giant luminous arcs, Einstein rings, the detection of dark matter and planets with lensing, time delays and the age of the universe (Hubble's constant), microlensing of stars and quasars. The main part of the book---Part III---employs the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation and solve certain key lensing problems. Results are published here for the first time. Mathematical topics discussed: Morse theory, Whitney singularity theory, Thom catastrophe theory, Mather stability theory, Arnold singularity theory, and the Euler characteristic via projectivized rotation numbers. These tools are applied to the study of stable lens systems, local and global geometry of caustics, caustic metamorphoses, multiple lensed images, lensed image magnification, magnification cross sections, and lensing by singular and nonsingular deflectors. Examples, illustrations, bibliography and index make this a suitable text for an undergraduate/graduate course, seminar, or independent thesis project on gravitational lensing. The book is also an excellent reference text for professional mathematicians, mathematical physicists, astrophysicists, and physicists.

Theoretical physicists allover the world are acquainted with Lande's celebrated computation of the g factor or splitting factor or, more precisely, the magne togyric factor. The so-called anomalous Zeeman effect had intrigued, if not vexed, some of the most distinguished physicists of that time, such as Bohr, Sommerfeld, Pauli, and others. Lande realized that this recalcitrant effect was inseparable from the multiplet line structure - a breakthrough in understanding which he achieved in 1922 at the age of thirty four. It was in the same year that Lande discovered the interval rule for the separation of multiplet sublevels, a significant result that holds in all cases of Russell-Saunders coupling and renders comparatively easy the empirical analysis of spectral multiplets. In the twenties, Lande succeeded in constructing some original concepts of axiomatic thermodynamics by employing Caratheodory's somewhat esoteric approach as his guiding concept. Published in the Handbuch der Physik, his comprehensive treatise, evincing several novel ideas, has become a classic. Lande, Sommerfeld's student though never a true disciple, published two monographs on quantum mechanics that are remarkable for their content and exposition. In this connection it may be apposite to stress that Lande had sub scribed for many years to the (infelicitously named) Copenhagen interpretation."

Aimed at senior undergraduate and first-year graduate students in departments of physics and astronomy, this textbook gives a systematic treatment of atomic and molecular structure and spectra, together with the effect of weak and strong external electromagnetic fields.
Topics chosen are those of interest in astronomy, and indeed many were inspired by specific astronomical contexts. Examples include the negative ion of hydrogen and the effects of strong magnetic fields such as those occurring on certain white dwarfs and neutron stars. Adiabatic and non-adiabatic handling of electron correlations and application to processes such as dielectronic recombination are included. Astronomical examples are provided throughout, as well as end-of-the-chapter problems and exercises. Over seventy illustrative diagrams complete this unique and comprehensive volume.

Quantum Neural Computation is a graduate level monographic textbook. It presents a comprehensive introduction, both non-technical and technical, into modern quantum neural computation, the science behind the fiction movie Stealth. Classical computing systems perform classical computations (i.e., Boolean operations, such as AND, OR, NOT gates) using devices that can be described classically (e.g., MOSFETs). On the other hand, quantum computing systems perform classical computations using quantum devices (quantum dots), that is devices that can be described only using quantum mechanics. Any information transfer between such computing systems involves a state measurement. This book describes this information transfer at the edge of classical and quantum chaos and turbulence, where mysterious quantum-mechanical linearity meets even more mysterious brain s nonlinear complexity, in order to perform a super high speed and error free computations. This monograph describes a crossroad between quantum field theory, brain science and computational intelligence."

The material collected in this book originated from the author's twenty-five years of teaching for a two-semester, first year graduate course in the University of Michigan. It discusses the physics and analysis of nuclear and electromagnetic interactions. It also introduces the concepts of Quantum Mechanics from the Liouville, rather than the Schroedinger, point of view. This viewpoint is unique, less abstract and lends itself nicely to physical applications. It is highly recommended as a text for graduate courses in Physics, Chemistry and Engineering.

The material collected in this book originated from the author's twenty-five years of teaching for a two-semester, first year graduate course in the University of Michigan. It discusses the physics and analysis of nuclear and electromagnetic interactions. It also introduces the concepts of Quantum Mechanics from the Liouville, rather than the Schroedinger, point of view. This viewpoint is unique, less abstract and lends itself nicely to physical applications. It is highly recommended as a text for graduate courses in Physics, Chemistry and Engineering.

Quantum theory is one of the most fascinating and successful constructs in the intellectual history of mankind. Nonetheless, the theory has very shaky philosophical foundations. This book contains thoughtful discussions by eminent researchers of a spate of experimental techniques newly developed to test some of the stranger predictions of quantum physics. The advances considered include recent experiments in quantum optics, electron and ion interferometry, photon down conversion in nonlinear crystals, single trapped ions interacting with laser beams, atom-field coupling in micromaser cavities, quantum computation, quantum cryptography, decoherence and macroscopic quantum effects, the quantum state diffusion model, quantum gravity, the quantum mechanics of cosmology and quantum non-locality along with the continuing debate surrounding the interpretation of quantum mechanics. Audience: The book is intended for physicists, philosophers of science, mathematicians, graduate students and those interested in the foundations of quantum theory.

This book is meant to be a text for a ?rst course in quantum physics. It is assumed that the student has had courses in Modern Physics and in mathematics through differential equations. The book is otherwise self-contained and does not rely on outside resources such as the internet to supplement the material. SI units are used throughoutexcept for those topics for which atomic units are especially convenient. It is our belief that for a physics major a quantum physics textbook should be more than a one- or two-semester acquaintance. Consequently, this book contains material that, while germane to the subject, the instructor might choose to omit because of time limitations. There are topics and examples included that are not normally covered in introductory textbooks. These topics are not necessarily too advanced, they are simply not usually covered. We have not, however, presumed to tell the instructor which topics must be included and which may be omitted. It is our intention that omitted subjects are available for future reference in a book that is already familiar to its owner. In short, it is our hope that the student will use the book as a reference after having completed the course. We have included at the end of most chapters a "Retrospective" of the chapter. Thisis notmeanttobemerelya summary, but, rather, anoverviewoftheimportance ofthe material andits placein the contextofpreviousandforthcomingchapters.

As miniaturisation deepens, and nanotechnology and its machines become more prevalent in the real world, the need to consider using quantum mechanical concepts to perform various tasks in computation increases. Such tasks include: the teleporting of information, breaking heretofore "unbreakable" codes, communicating with messages that betray eavesdropping, and the generation of random numbers. This is the first book to apply quantum physics to the basic operations of a computer, representing the ideal vehicle for explaining the complexities of quantum mechanics to students, researchers and computer engineers, alike, as they prepare to design and create the computing and information delivery systems for the future. Both authors have solid backgrounds in the subject matter at the theoretical and more practical level. While serving as a text for senior/grad level students in computer science/physics/engineering, this book has its primary use as an up-to-date reference work in the emerging interdisciplinary field of quantum computing - the only prerequisite being knowledge of calculus and familiarity with the concept of the Turing machine.

It has been said that String theorists talk to string theorists and everyone else wonders what they are saying'. This book will be a great help to those researchers who are challenged by modern quantum field theory. Quantum field theory experienced a renaissance in the late 1960s. Here, participants in the Les Houches sessions of 1970/75, now key players in quantum field theory and its many impacts, assess developments in their field of interest and provide guidance to young researchers challenged by these developments, but overwhelmed by their complexities. The book is not a textbook on string theory, rather it is a complement to Polchinski's book on string theory. It is a survey of current problems which have their origin in quantum field theory.

Classical Mechanics teaches readers how to solve physics problems; in other words, how to put math and physics together to obtain a numerical or algebraic result and then interpret these results physically. These skills are important and will be needed in more advanced science and engineering courses. However, more important than developing problem-solving skills and physical-interpretation skills, the main purpose of this multi-volume series is to survey the basic concepts of classical mechanics and to provide the reader with a solid understanding of the foundational content knowledge of classical mechanics. Classical Mechanics: Newton's Laws and Uniform Circular Motion focuses on the question: 'Why does an object move?'. To answer that question, we turn to Isaac Newton. The hallmark of any good introductory physics series is its treatment of Newton's laws of motion. These laws are difficult concepts for most readers for a number of reasons: they have a reputation as being difficult concepts; they require the mastery of multiple sub-skills; and problems involving these laws can be cast in a variety of formats.

Waves represent a classic topic of study in physics, mathematics, and engineering. Many modern technologies are based on our understanding of waves and their interaction with matter. In the past thirty years there have been some revolutionary developments in the study of waves. The present volume is the only available source which details these developments in a systematic manner, with the aim of reaching a broad audience of non-experts. It is an important resource book for those interested in understanding the physics underlying nanotechnology and mesoscopic phenomena, as well as for bridging the gap between the textbooks and research frontiers in any wave related topic. A special feature of this volume is the treatment of classical and quantum mechanical waves within a unified framework, thus facilitating an understanding of similarities and differences between the two.

Ever since its invention in 1929 the Dirac equation has played a fundamental role in various areas of modern physics and mathematics. Its applications are so widespread that a description of all aspects cannot be done with sufficient depth within a single volume. In this book the emphasis is on the role of the Dirac equation in the relativistic quantum mechanics of spin-1/2 particles. We cover the range from the description of a single free particle to the external field problem in quantum electrodynamics. Relativistic quantum mechanics is the historical origin of the Dirac equation and has become a fixed part of the education of theoretical physicists. There are some famous textbooks covering this area. Since the appearance of these standard texts many books (both physical and mathematical) on the non relativistic Schrodinger equation have been published, but only very few on the Dirac equation. I wrote this book because I felt that a modern, comprehensive presentation of Dirac's electron theory satisfying some basic requirements of mathematical rigor was still missing."