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Spinors In Hilbert Space
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Book Synopsis Spinors in Hilbert Space by : Paul Dirac
Download or read book Spinors in Hilbert Space written by Paul Dirac and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Hilbert Space The words "Hilbert space" here will always denote what math ematicians call a separable Hilbert space. It is composed of vectors each with a denumerable infinity of coordinates ql' q2' Q3, .... Usually the coordinates are considered to be complex numbers and each vector has a squared length ~rIQrI2. This squared length must converge in order that the q's may specify a Hilbert vector. Let us express qr in terms of real and imaginary parts, qr = Xr + iYr' Then the squared length is l:.r(x; + y;). The x's and y's may be looked upon as the coordinates of a vector. It is again a Hilbert vector, but it is a real Hilbert vector, with only real coordinates. Thus a complex Hilbert vector uniquely determines a real Hilbert vector. The second vector has, at first sight, twice as many coordinates as the first one. But twice a denumerable in finity is again a denumerable infinity, so the second vector has the same number of coordinates as the first. Thus a complex Hilbert vector is not a more general kind of quantity than a real one.
Book Synopsis Spinors in Hilbert Space by : Paul Adrien Maurice Dirac
Download or read book Spinors in Hilbert Space written by Paul Adrien Maurice Dirac and published by . This book was released on 1970 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spinors in Hilbert Space by : Roger Plymen
Download or read book Spinors in Hilbert Space written by Roger Plymen and published by Cambridge University Press. This book was released on 1994-12 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: A definitive self-contained account of the subject. Of appeal to a wide audience in mathematics and physics.
Book Synopsis Theory Of Spinors: An Introduction by : Moshe Carmeli
Download or read book Theory Of Spinors: An Introduction written by Moshe Carmeli and published by World Scientific Publishing Company. This book was released on 2000-04-12 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spinors are used extensively in physics. It is widely accepted that they are more fundamental than tensors, and the easy way to see this is through the results obtained in general relativity theory by using spinors — results that could not have been obtained by using tensor methods only.The foundation of the concept of spinors is groups; spinors appear as representations of groups. This textbook expounds the relationship between spinors and representations of groups. As is well known, spinors and representations are both widely used in the theory of elementary particles.The authors present the origin of spinors from representation theory, but nevertheless apply the theory of spinors to general relativity theory, and part of the book is devoted to curved space-time applications.Based on lectures given at Ben Gurion University, this textbook is intended for advanced undergraduate and graduate students in physics and mathematics, as well as being a reference for researchers.
Book Synopsis Spinors in Hilbert Space and the Infinite Orthogonal Group by : Derrick Corson Niederman
Download or read book Spinors in Hilbert Space and the Infinite Orthogonal Group written by Derrick Corson Niederman and published by . This book was released on 1981 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Theory of Spinors by : Élie Cartan
Download or read book The Theory of Spinors written by Élie Cartan and published by Courier Corporation. This book was released on 2012-04-30 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities.
Author :Gerardo F. Torres del Castillo Publisher :Springer Science & Business Media ISBN 13 :0817649840 Total Pages :182 pages Book Rating :4.8/5 (176 download)
Book Synopsis Spinors in Four-Dimensional Spaces by : Gerardo F. Torres del Castillo
Download or read book Spinors in Four-Dimensional Spaces written by Gerardo F. Torres del Castillo and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensional spaces with any signature. Some of the useful applications of four-dimensional spinors, such as Yang–Mills theory, are derived in detail using illustrative examples. Spinors in Four-Dimensional Spaces is aimed at graduate students and researchers in mathematical and theoretical physics interested in the applications of the two-component spinor formalism in any four-dimensional vector space or Riemannian manifold with a definite or indefinite metric tensor. This systematic and self-contained book is suitable as a seminar text, a reference book, and a self-study guide.
Download or read book Spinors in Physics written by Jean Hladik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Symplectic Dirac Operators by : Katharina Habermann
Download or read book Introduction to Symplectic Dirac Operators written by Katharina Habermann and published by Springer. This book was released on 2006-10-28 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.
Book Synopsis The Spinorial Chessboard by : Paolo Budinich
Download or read book The Spinorial Chessboard written by Paolo Budinich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spinor theory is an important tool in mathematical physics in particular in the context of conformal field theory and string theory. These lecture notes present a new way to introduce spinors by exploiting their intimate relationship to Clifford algebras. The presentation is detailed and mathematically rigorous. Not only students but also researchers will welcome this book for the clarity of its style and for the straightforward way it applies mathematical concepts to physical theory.
Book Synopsis Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields by : Roger Penrose
Download or read book Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields written by Roger Penrose and published by Cambridge University Press. This book was released on 1984 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1 introduces and systematically develops the calculus in a first detailed exposition of this technique which provides shortcuts for some very tedious calculations.
Book Synopsis An Introduction to Spinors and Geometry with Applications in Physics by : Ian M. Benn
Download or read book An Introduction to Spinors and Geometry with Applications in Physics written by Ian M. Benn and published by Institute of Physics Publishing (GB). This book was released on 1987 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: "...The aim of this book is to introduce theoretical physicists, of graduate student level upwards, to the methods of differential geometry and Clifford algebras in classical field theory..."--back cover.
Book Synopsis Spinors In Physics And Geometry by : Giuseppe Furlan
Download or read book Spinors In Physics And Geometry written by Giuseppe Furlan and published by World Scientific. This book was released on 1988-11-01 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference brought together physicists and mathematicians working on spinors, which have played an important role in recent research on supersymmetry, Kaluza-Klein theories, twistors and general relativity.
Book Synopsis Theory of Spinors and Its Application in Physics and Mechanics by : Vladimir A. Zhelnorovich
Download or read book Theory of Spinors and Its Application in Physics and Mechanics written by Vladimir A. Zhelnorovich and published by Springer Nature. This book was released on 2019-10-24 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a systematic exposition of the theory of spinors in finite-dimensional Euclidean and Riemannian spaces. The applications of spinors in field theory and relativistic mechanics of continuous media are considered. The main mathematical part is connected with the study of invariant algebraic and geometric relations between spinors and tensors. The theory of spinors and the methods of the tensor representation of spinors and spinor equations are thoroughly expounded in four-dimensional and three-dimensional spaces. Very useful and important relations are derived that express the derivatives of the spinor fields in terms of the derivatives of various tensor fields. The problems associated with an invariant description of spinors as objects that do not depend on the choice of a coordinate system are addressed in detail. As an application, the author considers an invariant tensor formulation of certain classes of differential spinor equations containing, in particular, the most important spinor equations of field theory and quantum mechanics. Exact solutions of the Einstein–Dirac equations, nonlinear Heisenberg’s spinor equations, and equations for relativistic spin fluids are given. The book presents a large body of factual material and is suited for use as a handbook. It is intended for specialists in theoretical physics, as well as for students and post-graduate students of physical and mathematical specialties.
Book Synopsis Introduction to 2-spinors in General Relativity by : Peter J. O'Donnell
Download or read book Introduction to 2-spinors in General Relativity written by Peter J. O'Donnell and published by World Scientific. This book was released on 2003 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Sample Chapter(s). Spinor Geometry (238 KB). Contents: Spinor Geometry; Spinor Algebra; Spinor Analysis; Lanczos Spinor. Readership: Postgraduate level students and researchers.
Download or read book Spin Geometry written by H. Blaine Lawson and published by Princeton University Press. This book was released on 2016-06-02 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds.
Book Synopsis Clifford Algebras and Spinor Structures by : Rafal Ablamowicz
Download or read book Clifford Algebras and Spinor Structures written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Albert Crumeyrolle, who died on June 17, 1992. In organizing the volume we gave priority to: articles summarizing Crumeyrolle's own work in differential geometry, general relativity and spinors, articles which give the reader an idea of the depth and breadth of Crumeyrolle's research interests and influence in the field, articles of high scientific quality which would be of general interest. In each of the areas to which Crumeyrolle made significant contribution - Clifford and exterior algebras, Weyl and pure spinors, spin structures on manifolds, principle of triality, conformal geometry - there has been substantial progress. Our hope is that the volume conveys the originality of Crumeyrolle's own work, the continuing vitality of the field he influenced, and the enduring respect for, and tribute to, him and his accomplishments in the mathematical community. It isour pleasure to thank Peter Morgan, Artibano Micali, Joseph Grifone, Marie Crumeyrolle and Kluwer Academic Publishers for their help in preparingthis volume.
