This book provides a representative sampling of the latest advances in theoretical physics. Chapters 1 and 2 deal with the Hydrogen atom. In Chapter 1, Blaive and Cadilhac carry out an analysis of hydrogenoid atomic wave functions. In Chapter 2, Boudet, Blaive Geniyes and Vanel carry out a relativistic calculation with retardation of the photoelectric effect of Hydrogen. Chapters 3 and 4 look at atoms in the presence of an external radiation field. Chapter 3 by Dastidar and Dastidar examines above-threshold ionisation of Argon in a laser field. In Chapter 4, Kazakov applies the Jaynes-Cummings model to an atom interacting simultaneously with a quasiresonant classical field and a quantised mode. Quantum dynamical problems are addressed in Chapters 5 and 6. In Chapter 5, Baute, Egusquiza and Muga study the effect of negative and classically-forbidden momenta in one-dimensional quantum scattering. Chapter 6 by Bellini finds analytical solutions to reaction-diffusion equations by mapping on a time-independent Schrödinger equation. Chapters 7 and 8 are devoted to nuclear and particle physics. In Chapter 7, Kravchenko and Soznik obtain the nucleon-nucleus optical potential in the nuclear matter approximation with the generalised Skyrme interaction. In Chapter 8, Terasaki examines non-factorisable contributions in decays. The final three chapters contain various mathematical studies which are of interest to theoretical physics in general. In Chapter 9, Shiqing analyses the equations of motion for the Newtonian n-body problem. Riazi looks at the geometry and topology of solitons in Chapter 10, and the book concludes with Chapter 11 containing a study by Elipe of the rotations of perturbed triaxial rigid bodies.

Today many important directions of research are being pursued more or less independently of each other. These are, for instance, strings and mem branes, induced gravity, embedding of spacetime into a higher dimensional space, the brane world scenario, the quantum theory in curved spaces, Fock Schwinger proper time formalism, parametrized relativistic quantum the ory, quantum gravity, wormholes and the problem of “time machines”, spin and supersymmetry, geometric calculus based on Clifford algebra, various interpretations of quantum mechanics including the Everett interpretation, and the recent important approach known as “decoherence”. A big problem, as I see it, is that various people thoroughly investigate their narrow field without being aware of certain very close relations to other fields of research. What we need now is not only to see the trees but also the forest. In the present book I intend to do just that: to carry out a first approximation to a synthesis of the related fundamental theories of physics. I sincerely hope that such a book will be useful to physicists. From a certain viewpoint the book could be considered as a course in the oretical physics in which the foundations of all those relevant fundamental theories and concepts are attempted to be thoroughly reviewed. Unsolved problems and paradoxes are pointed out. I show that most of those ap proaches have a common basis in the theory of unconstrained membranes. The very interesting and important concept of membrane space, the tensor calculus in and functional transformations in are discussed.

Proceedings of the NATO Advanced Research Workshop, Alushta, Crimea, Ukraine, from 31 August to 6 September 2002

The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.

A comprehensive and up-to-date overview of soft and hard diffraction processes in strong interaction physics. The first part covers soft hadron—hadron scattering in a complete and mature presentation. It can be used as a textbook in particle physics classes. Chapters 8-11 address graduate students as well as researchers, covering the "new diffraction": the pomeron in QCD, low-x physics, diffractive deep inelastic scattering and related processes.

Frank Wilczek is one of the foremost theoretical physicists of the past half-century. He has made several fundamental contributions that shape our understanding of high energy physics, cosmology, condensed matter physics, and statistical physics. In all these fields his many discoveries continue to play a key role in shaping the direction of modern theoretical physics.Among Wilczek's major achievements is the discovery of asymptotic freedom, which predicts and explains the ultraviolet behavior of non-abelian gauge theories. The axion, which he co-discovered and named, has emerged as the prevalent candidate for explaining the origin of dark matter in the Universe. His invention of color-flavor locking explains chiral symmetry breaking in high density quantum chromodynamics. His introduction of fractional statistics and anyons are pivotal to our understanding of the fractional quantum Hall effect and form the building blocks of topological quantum computing. His invention of the time crystal concept has catalyzed extensive investigations of dynamical phases of physical systems.Frank Wilczek received the 2004 Nobel Prize in Physics for the discovery of asymptotic freedom. He is also the recipient of several Prizes and honorary awards including the MacArthur Fellowship, the Lorentz Medal of the Royal Netherlands Academy of Arts and Sciences, the Lilienfeld Prize of the American Physical Society, the High Energy and Particle Physics Prize of the European Physical Society, and the King Faisal International Prize for Science of the King Faisal Foundation. He is a member of the National Academy of Sciences, American Academy of Arts and Sciences, and the American Philosophical Society. He is also a foreign member of the Royal Netherlands Academy of Arts and Sciences and of the Royal Academy of Sciences in Sweden.He is currently the Herman Feshbach Professor of Physics at MIT Center for Theoretical Physics. He also holds a professorship at Stockholm University, is a Distinguished Professor at Arizona State University, and is the founding director of the Tsung-Dao Lee Institute and Chief Scientist of the Wilczek Quantum Center at Shanghai Jiao Tong University.This volume serves as a tribute to Frank Wilczek's legendary scientific contributions, commemorating his 70th birthday and the first 50 years of his career as a theoretical physicist. The contributors include several of his PhD students, close collaborators, and both past and present colleagues.

New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.

The book collects a series of papers centered on two main streams: Feynman path integral approach to Quantum Mechanics and statistical mechanics of quantum open systems. Key authors discuss the state-of-the-art within their fields of expertise. In addition, the volume includes a number of contributed papers with new results, which have been thoroughly refereed.The contributions in this volume highlight emergent research in the area of stochastic analysis and mathematical physics, focusing, in particular on Feynman functional integral approach and, on the other hand, in quantum probability. The book is addressed to an audience of mathematical physicists, as well as specialists in probability theory, stochastic analysis and operator algebras.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.