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The Dirac operator has many useful applications in theoretical physics and mathematics. This book provides a clear, concise and self-contained introduction to the global theory of the Dirac operator and to the analysis of spectral asymptotics with local or nonlocal boundary conditions. The theory is introduced at a level suitable for graduate students. Numerous examples are then given to illustrate the peculiar properties of the Dirac operator, and the role of boundary conditions in heat-kernel asymptotics and quantum field theory. Topics covered include the introduction of spin-structures in...

This text provides a thoroughly modern graduate-level introduction to the theory of critical behavior. Beginning with a brief review of phase transitions in simple systems and of mean field theory, the text then goes on to introduce the core ideas of the renormalization group. Following chapters cover phase diagrams, fixed points, cross-over behavior, finite-size scaling, perturbative renormalization methods, low-dimensional systems, surface critical behavior, random systems, percolation, polymer statistics, critical dynamics and conformal symmetry. The book closes with an appendix on...

This timely review provides a self-contained introduction to the mathematical theory of stationary black holes and a self-consistent exposition of the corresponding uniqueness theorems. The opening chapters examine the general properties of space-times admitting Killing fields and derive the Kerr-Newman metric. Heusler emphasizes the general features of stationary black holes, the laws of black hole mechanics, and the geometrical concepts behind them. Tracing the steps toward the proof of the "no-hair" theorem, he illustrates the methods used by Israel, the divergence formulas derived by...

This is a comprehensive introduction to lattice models of polymers, an important topic both in the theory of critical phenomena and the modeling of polymers. The first two chapters introduce the basic theory of random, directed and self-avoiding walks. The book then goes on to develop and expand this theory to explore the self-avoiding walk in both two and three dimensions. Following chapters describe polymers near a surface, dense polymers, self interacting polymers and branched polymers. The book closes with discussions of some geometrical and topological properties of polymers, and of...

This book shows how modern cosmology and astronomy have led to the need to introduce dark matter in the universe to account for mass. Some of this dark matter is in the familiar form of protons, electrons and neutrons, but most of it must have a more exotic form. The favored, but not the only, possibility is neutrinos of non-zero rest mass, pair-created in the hot big bang and surviving to the present day. After a review of modern cosmology, this book gives a detailed account of the author's recent theory in which these neutrinos decay into photons that are the main ionizing agents in...