The theorems of Hawking and Penrose show that space-times are likely to contain incomplete geodesics. Such geodesics are said to end at a singularity if it is impossible to continue the space-time and geodesic without violating the usual topological and smoothness conditions on the space-time. In this book the different possible singularities are defined, and the mathematical methods needed to extend the space-time are described in detail. The results obtained (many appearing here for the first time) show that singularities are associated with a lack of smoothness in the Riemann tensor. While...
The theorems of Hawking and Penrose show that space-times are likely to contain incomplete geodesics. Such geodesics are said to end at a singularity ...
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...
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 dar...
This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. The book begins with a brief review of some aspects of Einstein's theory of relativity that are of particular importance for field theory, before going on to consider the relativistic quantum mechanics of free particles, interacting fields, and particles with spin. The techniques...
This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to mak...
Devoted to an important and popular branch of modern theoretical and mathematical physics, this book introduces the use of Lie algebra and differential geometry methods to study nonlinear integrable systems of Toda type. Many challenging problems in theoretical physics are related to the solution of nonlinear systems of partial differential equations. One of the most fruitful approaches in recent years has resulted from a merging of group algebraic and geometric techniques. The book gives a comprehensive introduction to this exciting branch of science. Chapters 1 and 2 review basic notions of...
Devoted to an important and popular branch of modern theoretical and mathematical physics, this book introduces the use of Lie algebra and differentia...
Self-organized criticality (SOC) maintains that complex behavior can develop spontaneously in certain multi-body systems whose dynamics vary abruptly. This is a clear and concise introduction to the field of self-organized criticality, and contains an overview of the main research results. The author begins with an examination of what is meant by SOC, and the systems in which it can occur. He then presents and analyzes computer models to describe a number of systems, explaining the different mathematical formalisms developed to understand SOC. The final chapter assesses the impact of this...
Self-organized criticality (SOC) maintains that complex behavior can develop spontaneously in certain multi-body systems whose dynamics vary abruptly....
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 text provides a thoroughly modern graduate-level introduction to the theory of critical behavior. Beginning with a brief review of phase transiti...
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 is a comprehensive introduction to lattice models of polymers, an important topic both in the theory of critical phenomena and the modeling of po...
This controversial book examines one of the most fundamental questions of modern cosmology: how much matter is there in the Universe? This issue affects theories of the origin and evolution of the Universe as well as its geometrical structure and ultimate fate. The authors address this debate and point out the most likely avenues for determining the actual density of Universe matter in both visible and invisible forms by pulling together evidence from all available sources. They conclude that the balance of arguments presently lies with a density of around twenty percent of the critical...
This controversial book examines one of the most fundamental questions of modern cosmology: how much matter is there in the Universe? This issue affec...
We inhabit a world of differences--cultural, religious, moral, philosophical. The question that preoccupies the contributors to this volume is whether the fact of difference--plurality--inevitably leads to the conclusion that there cannot be a single truth, even in moral matters. The collection brings together a wide variety of contributors with different backgrounds and distinctive skills and attitudes to explore the implications of plurality, and no reader will be left in any doubt that the issues are fundamental ones.
We inhabit a world of differences--cultural, religious, moral, philosophical. The question that preoccupies the contributors to this volume is whether...
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...
The Dirac operator has many useful applications in theoretical physics and mathematics. This book provides a clear, concise and self-contained introdu...