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Spinors In Four Dimensional Spaces
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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.
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.
Author :Gerardo F. Torres del Castillo Publisher :Springer Science & Business Media ISBN 13 :0817681469 Total Pages :256 pages Book Rating :4.8/5 (176 download)
Book Synopsis 3-D Spinors, Spin-Weighted Functions and their Applications by : Gerardo F. Torres del Castillo
Download or read book 3-D Spinors, Spin-Weighted Functions and their Applications written by Gerardo F. Torres del Castillo and published by Springer Science & Business Media. This book was released on 2012-09-07 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Theory of Spinors and Its Application in Physics and Mechanics by : Vladimir Arkadʹevich Zhelnorovich
Download or read book Theory of Spinors and Its Application in Physics and Mechanics written by Vladimir Arkadʹevich Zhelnorovich and published by . This book was released on 2019 with total page 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 Heisenbergs 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.
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 The Theory of Spinors by : Elie Cartan
Download or read book The Theory of Spinors written by Elie Cartan and published by Courier Corporation. This book was released on 1981-02-01 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: The French mathematician Élie Cartan (1869–1951) was one of the founders of the modern theory of Lie groups, a subject of central importance in mathematics and also one with many applications. In this volume, he describes the orthogonal groups, either with real or complex parameters including reflections, and also the related groups with indefinite metrics. He develops the theory of spinors (he discovered the general mathematical form of spinors in 1913) systematically by giving a purely geometrical definition of these mathematical entities; this geometrical origin makes it very easy to introduce spinors into Riemannian geometry, and particularly to apply the idea of parallel transport to these geometrical entities. The book is divided into two parts. The first is devoted to generalities on the group of rotations in n-dimensional space and on the linear representations of groups, and to the theory of spinors in three-dimensional space. Finally, the linear representations of the group of rotations in that space (of particular importance to quantum mechanics) are also examined. The second part is devoted to the theory of spinors in spaces of any number of dimensions, and particularly in the space of special relativity (Minkowski space). While the basic orientation of the book as a whole is mathematical, physicists will be especially interested in the final chapters treating the applications of spinors in the rotation and Lorentz groups. In this connection, Cartan shows how to derive the "Dirac" equation for any group, and extends the equation to general relativity. One of the greatest mathematicians of the 20th century, Cartan made notable contributions in mathematical physics, differential geometry, and group theory. Although a profound theorist, he was able to explain difficult concepts with clarity and simplicity. In this detailed, explicit treatise, mathematicians specializing in quantum mechanics will find his lucid approach a great value.
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 On the Application of Spinors to the Problems of Celestial Mechanics by : Karl Stumpff
Download or read book On the Application of Spinors to the Problems of Celestial Mechanics written by Karl Stumpff and published by . This book was released on 1968 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometry, Topology and Quantum Field Theory by : P. Bandyopadhyay
Download or read book Geometry, Topology and Quantum Field Theory written by P. Bandyopadhyay and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph on geometrical and topological features which arise in quantum field theory. It is well known that when a chiral fermion interacts with a gauge field we have chiral anomaly which corresponds to the fact that divergence of the axial vector current does not vanish. It is observed that this is related to certain topological features associated with the fermion and leads to the realization of the topological origin of fermion number as well as the Berry phase. The role of gauge fields in the quantization procedure has its implications in these topological features of a fermion and helps us to consider a massive fermion as a soliton (skyrrnion). In this formalism chiral anomaly is found to be responsible for mass generation. This has its relevance in electroweak theory where it is observed that weak interaction gauge bosons attain mass topologically. The geometrical feature of a skyrmion also helps us to realize the internal symmetry of hadrons from reflection group. Finally it has been shown that noncommutative geometry where the space time manifold is taken to be X = M x Zz has its relevance in the description of a massive 4 fermion as a skyrmion when the discrete space is considered as the internal space and the symmetry breaking leads to chiral anomaly. In chap. l preliminary mathematical formulations related to the spinor structure have been discussed. In chap.
Book Synopsis Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry by : Roger Penrose
Download or read book Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry written by Roger Penrose and published by Cambridge University Press. This book was released on 1984 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant methods may be used to elucidate the structure and properties of space-time. In volume 1, Two-spinor calculus and relativistic fields, the calculus of 2-spinors is introduced and developed. Volume 2, Spinor and twistor methods in space-time geometry, introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. This work will be of great value to all those studying relativity, differential geometry, particle physics and quantum field theory from beginning graduate students to experts in these fields.
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 Classical Field Theory by : Horaƫiu Năstase
Download or read book Classical Field Theory written by Horaƫiu Năstase and published by Cambridge University Press. This book was released on 2019-03-14 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to classical field theory focusing on methods and solutions, providing a foundation for the study of quantum field 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 B-Model Gromov-Witten Theory by : Emily Clader
Download or read book B-Model Gromov-Witten Theory written by Emily Clader and published by Springer. This book was released on 2019-04-08 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects various perspectives, contributed by both mathematicians and physicists, on the B-model and its role in mirror symmetry. Mirror symmetry is an active topic of research in both the mathematics and physics communities, but among mathematicians, the “A-model” half of the story remains much better-understood than the B-model. This book aims to address that imbalance. It begins with an overview of several methods by which mirrors have been constructed, and from there, gives a thorough account of the “BCOV” B-model theory from a physical perspective; this includes the appearance of such phenomena as the holomorphic anomaly equation and connections to number theory via modularity. Following a mathematical exposition of the subject of quantization, the remainder of the book is devoted to the B-model from a mathematician’s point-of-view, including such topics as polyvector fields and primitive forms, Givental’s ancestor potential, and integrable systems.
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.
Book Synopsis Quantum Fields and Strings: A Course for Mathematicians by : Pierre Deligne
Download or read book Quantum Fields and Strings: A Course for Mathematicians written by Pierre Deligne and published by American Mathematical Society. This book was released on 1999-10-25 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.
Book Synopsis Representations of the Rotation and Lorentz Groups and Their Applications by : I. M. Gelfand
Download or read book Representations of the Rotation and Lorentz Groups and Their Applications written by I. M. Gelfand and published by Courier Dover Publications. This book was released on 2018-04-18 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph on the description and study of representations of the rotation group of three-dimensional space and of the Lorentz group features advanced topics and techniques crucial to many areas of modern theoretical physics. Prerequisites include a familiarity with the differential and integral calculus of several variables and the fundamentals of linear algebra. Suitable for advanced undergraduate and graduate students in mathematical physics, the book is also designed for mathematicians studying the representations of Lie groups, for whom it can serve as an introduction to the general theory of representation. The treatment encompasses all the basic material of the theory of representations used in quantum mechanics. The two-part approach begins with representations of the group of rotations of three-dimensional space, analyzing the rotation group and its representations. The second part, covering representations of the Lorentz group, includes an exploration of relativistic-invariant equations. The text concludes with three helpful supplements and a bibliography.
