تحسين النتائح
ترتيب حسب
من
الى
الصفحة 1
الصفحة 1
Loop Spaces, Characteristic Classes and Geometric Quantization
This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Various developments in mathematical physics (e.g., in knot theory, gauge theory, and topological quantum field theory) have led mathematicians and physicists to search for new geometric structures on manifolds and to seek a synthesis of ideas from geometry, topology and category theory. In this spirit, this book develops the differential geometry associated to the topology and obstruction theory of certain fiber bundles (more precisely, associated to grebes). The theory is a 3-dimensional analog of the familiar Kostant--Weil theory of line bundles. In particular the curvature now becomes a 3-form.
Lie Theory Vol.229 : Unitary Representations and Compactifications of Symmetric Spaces
It focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications; and branching laws for unitary representations, i.e., restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles.Ji's introductory chapter motivates the subject of symmetric spaces and their compactifications with carefully selected examples. A discussion of Satake and Furstenberg boundaries and a survey of the geometry of Riemannian symmetric spaces in general provide a good background for the second chapter, namely, the Borel–Ji authoritative treatment of various types of compactifications useful for studying symmetric and locally symmetric spaces. Borel–Ji further examine constructions of Oshima, De Concini, Procesi, and Melrose, which demonstrate the wide applicability of compactification techniques. Kobayashi examines the important subject of branching laws. Important concepts from modern representation theory, such as Harish–Chandra modules, associated varieties, microlocal analysis, derived functor modules, and geometric quantization are introduced. Concrete examples and relevant exercises engage the reader.
Lectures on Quantum Mechanics
Presents theoretical physics with a breathtaking array of examples and anecdotes. Basdevant's style is clear and stimulating, in the manner of a brisk classroom lecture that students can follow with ease and enjoyment.
Chiral Soliton Models for Baryons
This concise research monograph introduces and reviews the concept of chiral soliton models for baryons. In these models, baryons emerge as (topological) defects of the chiral field. The many applications shed light on a number of bayron properties, ranging from static properties via nucleon resonances and deep inelastic scattering to even heavy ion collisions. As far as possible, the theoretical investigations are confronted with experiment. Conceived to bridge the gap between advanced graduate textbooks and the research literature, this volume also features a number of appendices to help nonspecialist readers to follow in more detail some of the calculations in the main text.
Advanced Quantum Mechanics
Discusses nonrelativistic multi-particle systems, relativistic wave equations and relativistic quantum fields. Characteristic of the author´s work are the comprehensive mathematical discussions in which all intermediate steps are derived and where numerous examples of application and exercises help the reader gain a thorough working knowledge of the subject. The topics treated in the book lay the foundation for advanced studies in solid-state physics, nuclear and elementary particle physics. This text both extends and complements Schwabl´s introductory Quantum Mechanics, which covers nonrelativistic quantum mechanics and offers a short treatment of the quantization of the radiation field. The fourth edition has been thoroughly revised with new material having been added. Furthermore, the layout of the figures has been unified, which should facilitate comprehension.
Advanced Quantum Mechanics
Advanced Quantum Mechanics, the second volume on quantum mechanics by Franz Schwabl, discusses nonrelativistic multi-particle systems, relativistic wave equations and relativistic fields. Characteristic of Schwabl’s work, this volume features a compelling mathematical presentation in which all intermediate steps are derived and where numerous examples for application and exercises help the reader to gain a thorough working knowledge of the subject. The treatment of relativistic wave equations and their symmetries and the fundamentals of quantum field theory lay the foundations for advanced studies in solid-state physics, nuclear and elementary particle physics. This text extends and complements Schwabl’s introductory Quantum Mechanics, which covers nonrelativistic quantum mechanics and offers a short treatment of the quantization of the radiation field. New material has been added to this third edition of Advanced Quantum Mechanics on Bose gases, the Lorentz covariance of the Dirac equation, and the ‘hole theory’ in the chapter "Physical Interpretation of the Solutions to the Dirac Equation."
A Mathematical Introduction to Conformal Field Theory
The first part of this book gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. In particular, the conformal groups are determined and the appearance of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. The second part surveys some more advanced topics of conformal field theory, such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface.
