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Geometric Algebra with Applications in Science and Engineering
The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hesten...
Computer Algebra and Geometric Algebra with Applications
MathematicsMechanization consistsoftheory,softwareandapplicationofc- puterized mathematical activities such as computing, reasoning and discovering. ItsuniquefeaturecanbesuccinctlydescribedasAAA(Algebraization,Algori- mization, Application). The name “Mathematics Mechanization” has its origin in the work of Hao Wang (1960s), one of the pioneers in using computers to do research in mathematics, particularly in automated theorem proving. Since the 1970s, this research direction has been actively pursued and extensively dev- oped by Prof. Wen-tsun Wu and his followers. It di?ers from the closely related disciplines like Computer Mathematics, Symbolic Computation and Automated Reasoning in t...
Clifford Algebras
The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.
Current Topics in Astrofundamental Physics: The Cosmic Microwave Background
This NATO Advanced Study Institute provided an up dated understanding, from a fundamental and deep point of view, of the progress and current problems in the early universe, cosmic microwave background radiation, large scale structure, dark matter problem, and the interplay between them. The focus was placed on the Cosmic Microwave Background Radiation. Emphasis was given to the mutual impact of fundamental physics and cosmology, both at theoretical and experimental-or observational-levels, within a deep and well defined programme, and a global unifying view, which, in addition, provides of careful inter-disciplinarity. Special Lectures were devoted to neutrinos in astrophysics and high ener...
Current Topics in Astrofundamental Physics
This NATO Advanced Study Institute course provided an updated understanding, from a fundamental and deep point of view, of the progress and current problems in the early universe, cosmic microwave background radiation, large-scale struc ture, dark matter problem, and the interplay between them. Emphasis was placed on the mutual impact of fundamental physics and cosmology, both at the theo retical and experimental or observational levels, within a deep and well defined programme, and a global unifying view, which, in addition, provides of careful inter-disciplinarity. In addition, each course of this series introduced and promoted topics or sub jects which, although not of a purely astrophysi...
General Relativity
General Relativity: An Introduction for Physicists provides a clear mathematical introduction to Einstein's theory of general relativity. It presents a wide range of applications of the theory, concentrating on its physical consequences. After reviewing the basic concepts, the authors present a clear and intuitive discussion of the mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are then used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is then introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle. Written for advanced undergraduate and graduate students, this approachable textbook contains over 300 exercises to illuminate and extend the discussion in the text.
Clifford Algebras and their Applications in Mathematical Physics
This International Conference on Clifford AlgebrfU and Their Application, in Math ematical Phy,ic, is the third in a series of conferences on this theme, which started at the Univer,ity of Kent in Canterbury in 1985 and was continued at the Univer,iU de, Science, et Technique, du Languedoc in Montpellier in 1989. Since the start of this series of Conferences the research fields under consideration have evolved quite a lot. The number of scientific papers on Clifford Algebra, Clifford Analysis and their impact on the modelling of physics phenomena have increased tremendously and several new books on these topics were published. We were very pleased to see old friends back and to wellcome new ...
The primordial universe - L'univers primordial
This book reviews the interconnection of cosmology and particle physics over the last decade. It provides introductory courses in supersymmetry, superstring and M-theory, responding to an increasing interest to evaluate the cosmological consequences of these theories. Based on a series of extended courses providing an introduction to the physics of the very early universe, in the light of the most recent advances in our understanding of the fundamental interactions, it reviews all the classical issues (inflation, primordial fluctuations, dark matter, baryogenesis), but also introduces the most recent ideas about what happened at the Big Bang, and before.
Clifford Algebras and their Applications in Mathematical Physics
The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.
Structure Formation in the Universe
This book contains a series of lectures given at the NATO Advanced Study Institute (ASI) "Structure Formation in the Universe", held at the Isaac Newton Institute in Cambridge in August, 1999. The ASI was held at a critical juncture in the development of physical cosmology, when a flood of new data concerning the large scale structure of the Universe was just be coming available. There was an air of excitement and anticipation: would the standard theories fit the data, or would new ideas and models be re quired? Cosmology has long been a field of common interest between East and West, with many seminal contributions made by scientists working in the former Soviet Union and Eastern bloc. A ma...
