Contents:Lectures on Algebraic Quantum Field Theory (J Roberts)Introduction to the Algebraic Theory of Superselection Sectors (D Kastler, M Mebkhout & K H Rehren)Localisability of Particle States (K Fredenhagen)Local Observables and the Structure of Quantum Field Theory (S Doplicher)Braid Group Statistics and Their Superselection Rules (K H Rehren)Principles of General Quantum Field Theory Versus New Intuition from Model Studies. An Essay on the Work of J A Swieca (B Schroer)Endomorphisms and Quantum Symmetry of the Conformal Ising Model (G Mack & V Schomerus)Superselection Sectors in Quantum Field Model: Kinks in Φ24 and Charged States in Lattice Q.E.D. (J Fröelich & P A Marchetti)Braid Statistics in 3-Dimensional Local Quantum Theory (J Fröelich, & F Gabbiani)Index Theory of Subfactors and Braid Group statistics (R Longo)Technical Properties of the Quasi-local Algebra (C D'Antoni)Localized Automorphisms of the U(1)-Current Algebra on the Circle. A Simple Example (D Buchholz, G Mack & I Todorov) Readership: High energy physicists, solid state physicists, mathematical physicists and mathematicians.

Conceptual progress in fundamental theoretical physics is linked with the search for the suitable mathematical structures that model the physical systems. Quantum field theory (QFT) has proven to be a rich source of ideas for mathematics for a long time. However, fundamental questions such as ``What is a QFT?'' did not have satisfactory mathematical answers, especially on spaces with arbitrary topology, fundamental for the formulation of perturbative string theory. This book contains a collection of papers highlighting the mathematical foundations of QFT and its relevance to perturbative string theory as well as the deep techniques that have been emerging in the last few years. The papers are organized under three main chapters: Foundations for Quantum Field Theory, Quantization of Field Theories, and Two-Dimensional Quantum Field Theories. An introduction, written by the editors, provides an overview of the main underlying themes that bind together the papers in the volume.

Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).