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Introduction To 2-spinors In General Relativity
This book deals with 2-spinors in general relativity, beginning by developing spinors in a geometrical way rather than using representation theory, which can be a little abstract. This gives the reader greater physical intuition into the way in which spinors behave. The book concentrates on the algebra and calculus of spinors connected with curved space-time. Many of the well-known tensor fields in general relativity are shown to have spinor counterparts. An analysis of the Lanczos spinor concludes the book, and some of the techniques so far encountered are applied to this. Exercises play an important role throughout and are given at the end of each chapter.
Spinors in Physics
Invented by Dirac in creating his relativistic quantum theory of the electron, spinors are important in quantum theory, relativity, nuclear physics, atomic and molecular physics, and condensed matter physics. Essentially, they are the mathematical entities that correspond to electrons in the same way that ordinary wave functions correspond to classical particles. Because of their relations to the rotation group SO(n) and the unitary group SU(n), this discussion will be of interest to applied mathematicians as well as physicists.
3-D Spinors, Spin-Weighted Functions and their Applications
This book on the theory of three-dimensional spinors and their applications fills an important gap in the literature. It gives an introductory treatment of spinors. From the reviews: "Gathers much of what can be done with 3-D spinors in an easy-to-read, self-contained form designed for applications that will supplement many available spinor treatments. The book...should be appealing to graduate students and researchers in relativity and mathematical physics." -—MATHEMATICAL REVIEWS
Clifford Algebra and Spinor-Valued Functions
This volume describes the substantial developments in Clifford analysis which have taken place during the last decade and, in particular, the role of the spin group in the study of null solutions of real and complexified Dirac and Laplace operators. The book has six main chapters. The first two (Chapters 0 and I) present classical results on real and complex Clifford algebras and show how lower-dimensional real Clifford algebras are well-suited for describing basic geometric notions in Euclidean space. Chapters II and III illustrate how Clifford analysis extends and refines the computational tools available in complex analysis in the plane or harmonic analysis in space. In Chapter IV the con...
Gravitation: Sl(2,c) Gauge Theory And Conservation Laws
This monograph gives a comprehensive presentation of the SL(2,C) Gauge Theory of Gravitation along with some recent developments in the problem of Conservation Laws in General Relativity. Emphasis is put on quadratic Lagrangians which yield the Einstein field equations, as compared with Hilbert's original linear Langrangian, thus gravitation follows the other Gauge Fields all of which are derived from nonlinear Lagrangians.
Einstein's Unification
Why did Einstein tirelessly study unified field theory for more than thirty years? In this book, the author argues that Einstein believed he could find a unified theory of all of nature's forces by repeating the methods he thought he had used when he formulated general relativity. The book discusses Einstein's route to the general theory of relativity, focusing on the philosophical lessons that he learnt. It then addresses his quest for a unified theory for electromagnetism and gravity, discussing in detail his efforts with Kaluza-Klein and, surprisingly, the theory of spinors. From these perspectives, Einstein's critical stance towards the quantum theory comes to stand in a new light. This book will be of interest to physicists, historians and philosophers of science.
The Wonder of Quantum Spin
The Wonder of Quantum Spin is a confection of the history and the science of quantum spin sprinkled with quotations and excerpts from pioneers who lived and breathed science. The book unfolds two centuries of the golden era in mathematics and physics, where first glimpses of spin appeared nearly 200 years ago in the mathematics of rotations. In these studies, spinors emerged as a new entity that changes sign after a 360 degree rotation, reminiscent of the Mobius geometry. A century later, quantum spins described by spinors was discovered in physics in atomic spectra. This led to the discovery of antimatter and raised the possibility of parity violation. It gave the first warning that protons...
Lorentz Group, CPT and Neutrinos
The topics in this volume range from mathematical aspects of the theory of the Poincar‚ group, Clifford algebras and the CPT theorem, through new theoretical physical constructions and concepts (such as the physical significance of the 4-potential, the interplay between quantum mechanics and gravity, Majorana-like models, the photon as a composite particle, action-at-a-distance and superluminal phenomena), to experiments in neutrino physics. The book will be of interest to graduate students and researchers working in fundamental physics and phenomenology, and also to experimentalists.
