Author: Ian M. Benn
Publisher: Institute of Physics Publishing (GB)
ISBN:
Category : Mathematics
Languages : en
Pages : 376
Book Description
"...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.
An Introduction to Spinors and Geometry with Applications in Physics
Author: Ian M. Benn
Publisher: Institute of Physics Publishing (GB)
ISBN:
Category : Mathematics
Languages : en
Pages : 376
Book Description
"...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.
Publisher: Institute of Physics Publishing (GB)
ISBN:
Category : Mathematics
Languages : en
Pages : 376
Book Description
"...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.
Theory Of Spinors: An Introduction
Author: Moshe Carmeli
Publisher: World Scientific Publishing Company
ISBN: 9813102764
Category : Science
Languages : en
Pages : 228
Book Description
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.
Publisher: World Scientific Publishing Company
ISBN: 9813102764
Category : Science
Languages : en
Pages : 228
Book Description
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.
Theory of Spinors and Its Application in Physics and Mechanics
Author: Vladimir A. Zhelnorovich
Publisher: Springer Nature
ISBN: 3030278360
Category : Science
Languages : en
Pages : 392
Book Description
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.
Publisher: Springer Nature
ISBN: 3030278360
Category : Science
Languages : en
Pages : 392
Book Description
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.
The Theory of Spinors
Author: Élie Cartan
Publisher: Courier Corporation
ISBN: 0486137325
Category : Mathematics
Languages : en
Pages : 193
Book Description
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.
Publisher: Courier Corporation
ISBN: 0486137325
Category : Mathematics
Languages : en
Pages : 193
Book Description
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.
An Introduction to Clifford Algebras and Spinors
Author: Jayme Vaz Jr.
Publisher: Oxford University Press
ISBN: 0191085782
Category : Science
Languages : en
Pages : 257
Book Description
This text explores how Clifford algebras and spinors have been sparking a collaboration and bridging a gap between Physics and Mathematics. This collaboration has been the consequence of a growing awareness of the importance of algebraic and geometric properties in many physical phenomena, and of the discovery of common ground through various touch points: relating Clifford algebras and the arising geometry to so-called spinors, and to their three definitions (both from the mathematical and physical viewpoint). The main point of contact are the representations of Clifford algebras and the periodicity theorems. Clifford algebras also constitute a highly intuitive formalism, having an intimate relationship to quantum field theory. The text strives to seamlessly combine these various viewpoints and is devoted to a wider audience of both physicists and mathematicians. Among the existing approaches to Clifford algebras and spinors this book is unique in that it provides a didactical presentation of the topic and is accessible to both students and researchers. It emphasizes the formal character and the deep algebraic and geometric completeness, and merges them with the physical applications. The style is clear and precise, but not pedantic. The sole pre-requisites is a course in Linear Algebra which most students of Physics, Mathematics or Engineering will have covered as part of their undergraduate studies.
Publisher: Oxford University Press
ISBN: 0191085782
Category : Science
Languages : en
Pages : 257
Book Description
This text explores how Clifford algebras and spinors have been sparking a collaboration and bridging a gap between Physics and Mathematics. This collaboration has been the consequence of a growing awareness of the importance of algebraic and geometric properties in many physical phenomena, and of the discovery of common ground through various touch points: relating Clifford algebras and the arising geometry to so-called spinors, and to their three definitions (both from the mathematical and physical viewpoint). The main point of contact are the representations of Clifford algebras and the periodicity theorems. Clifford algebras also constitute a highly intuitive formalism, having an intimate relationship to quantum field theory. The text strives to seamlessly combine these various viewpoints and is devoted to a wider audience of both physicists and mathematicians. Among the existing approaches to Clifford algebras and spinors this book is unique in that it provides a didactical presentation of the topic and is accessible to both students and researchers. It emphasizes the formal character and the deep algebraic and geometric completeness, and merges them with the physical applications. The style is clear and precise, but not pedantic. The sole pre-requisites is a course in Linear Algebra which most students of Physics, Mathematics or Engineering will have covered as part of their undergraduate studies.
Spinors In Physics And Geometry
Author: Giuseppe Furlan
Publisher: World Scientific
ISBN: 9814644447
Category :
Languages : en
Pages : 368
Book Description
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.
Publisher: World Scientific
ISBN: 9814644447
Category :
Languages : en
Pages : 368
Book Description
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.
Geometry, Spinors and Applications
Author: Donal J. Hurley
Publisher: Springer
ISBN: 1852332239
Category : Science
Languages : en
Pages : 392
Book Description
This text is a self-contained, comprehensive treatment of the tensor and spinor calculus of space-time manifolds with as few technicalities as correct treatment allows. Both the physical and geometrical motivation of all concepts are discussed, helping the reader to go through the technical details in a confident manner. Several physical theories are discussed and developed beyond standard treatment using results in the book. Both the traditional "index" and modern "coordinate-free" notations are used side-by-side in the book, making it accessible to beginner graduate students in mathematics and physics. The methods developed offer new insights into standard areas of physics, such as classical mechanics or electromagnetism, and takes readers to the frontiers of knowledge of spinor calculus.
Publisher: Springer
ISBN: 1852332239
Category : Science
Languages : en
Pages : 392
Book Description
This text is a self-contained, comprehensive treatment of the tensor and spinor calculus of space-time manifolds with as few technicalities as correct treatment allows. Both the physical and geometrical motivation of all concepts are discussed, helping the reader to go through the technical details in a confident manner. Several physical theories are discussed and developed beyond standard treatment using results in the book. Both the traditional "index" and modern "coordinate-free" notations are used side-by-side in the book, making it accessible to beginner graduate students in mathematics and physics. The methods developed offer new insights into standard areas of physics, such as classical mechanics or electromagnetism, and takes readers to the frontiers of knowledge of spinor calculus.
An Introduction to Clifford Algebras and Spinors
Author: Jayme Vaz Jr.
Publisher: Oxford University Press
ISBN: 0198782926
Category : Mathematics
Languages : en
Pages : 257
Book Description
This work is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.
Publisher: Oxford University Press
ISBN: 0198782926
Category : Mathematics
Languages : en
Pages : 257
Book Description
This work is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.
An Introduction to Twistor Theory
Author: S. A. Huggett
Publisher: Cambridge University Press
ISBN: 9780521456890
Category : Mathematics
Languages : en
Pages : 196
Book Description
Evolving from graduate lectures given in London and Oxford, this introduction to twistor theory and modern geometrical approaches to space-time structure will provide graduate students with the basics of twistor theory, presupposing some knowledge of special relativity and differenttial geometry.
Publisher: Cambridge University Press
ISBN: 9780521456890
Category : Mathematics
Languages : en
Pages : 196
Book Description
Evolving from graduate lectures given in London and Oxford, this introduction to twistor theory and modern geometrical approaches to space-time structure will provide graduate students with the basics of twistor theory, presupposing some knowledge of special relativity and differenttial geometry.
Spinors in Four-Dimensional Spaces
Author: Gerardo F. Torres del Castillo
Publisher: Springer Science & Business Media
ISBN: 0817649840
Category : Mathematics
Languages : en
Pages : 182
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 0817649840
Category : Mathematics
Languages : en
Pages : 182
Book Description
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.