Lecture Notes

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. Strong emphasis is given to the geometrical concepts. The general features of stationary black holes and the laws of black hole mechanics are then reviewed. Critical steps towards the proof of the 'no-hair' theorem are then discussed, including the methods used by Israel, the divergence formulae derived by Carter, Robinson and others, and finally the sigma model identities and the positive mass theorem. The book is rounded off with an extension of the electro-vacuum uniqueness theorem to self-gravitating scalar fields and harmonic mappings. This volume provides a rigorous textbook for graduate students in physics and mathematics. It also offers an invaluable, up-to-date referenc

Complex Finsler metrics appear naturally in complex analysis. To develop new tools in this area, the book provides a graduate-level introduction to differential geometry of complex Finsler metrics. Af

This author provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. His aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules. 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 learnt in the chapters are then demonstrated in examples that might be encountered in real accelerator physics. Further chapters contain discussions of renormalization, massive and massless vector fields and unitarity. A final chapter presents concluding arguments concerning quantum electrodynamics. The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and di

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 Friedmann singularity is analysed as an example, the emphasis is on general theorems and techniques rather than on the classification of particular exact solutions.

This book shows how modern cosmology and astronomy have led to the need to introduce dark matter in the universe. 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 favoured, 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 which are the main ionising agents in hydrogen and nitrogen in the interstellar and intergalactic medium. This theory, though speculative, explains a number of rather different puzzling phenomena in astronomy and cosmology in a unified way and predicts values of various important quantities such as the mass of the decaying neutrino and the Hubble constant. Written by a cosmologist of the first rank, this topical book will be essential reading to all cosmologis

Experts in operations research and developers of softwareapplication systems have been treading separate paths formany years. It is urgently necessary to reset this course sothat the demanding require

This monograph is intended for an advanced undergraduate or graduate course as well as for researchers, who want a compilation of developments in this rapidly growing field of operations research. Thi

Discusses the physical consequences of the symmetries of the Wigner function in phase space, for scientists and students who wish to study the basic principles of the phase-space picture of quantum me

Narison (Laboratoire de Physique Mathematique of Montpellier) provides an elementary introduction to the method of QCD spectral sum rules (QSSR) for non-specialists and experimental physicists, and a

The lecture notes presented in these pages were originally developed for use in the Energy Management Training Program (EMTP), sponsored by the Office of Energy, U. S. Agency for International Develop

Since quasi-uniform spaces were defined in 1948, a diverse and widely dispersed literatureconcerning them has emerged. In Quasi-Uniform Spaces, the authors present a comprehensivestudy of these struct

These lecture notes comprise a three-semester graduate course in quantum mechanics at the University of Illinois. There are a number of texts which present the basic topics very well; but since a fair quantity of the material discussed in my course was not available to the students in elementary quantum mechanics books, I was asked to prepare written notes. In retrospect these lecture notes seemed sufficiently interesting to warrant their publication in this format. The notes, presented here in slightly revised form, consitutute a self-contained course in quantum mechanics from first principles to elementary and relativistic one-particle mechanics. Prerequisite to reading these notes is some familiarity with elementary quantum mechanics, at least at the undergraduate level. Preferably the reader should already have met the uncertainty principle and the concept of a wave function. Prerequisites also include sufficient acquaintance with complex cariables to be able to do simple contour i