An Introduction To Spinors And Geometry With Applications In Physics

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An Introduction To Spinors And Geometry With Applications In Physics

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Author : Ian M. Benn
language : en
Publisher: Institute of Physics Publishing (GB)
Release Date : 1987

An Introduction To Spinors And Geometry With Applications In Physics written by Ian M. Benn and has been published by Institute of Physics Publishing (GB) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.

"...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 Clifford Algebras And Spinors

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Author : Jayme Vaz Jr.
language : en
Publisher: Oxford University Press
Release Date : 2016

An Introduction To Clifford Algebras And Spinors written by Jayme Vaz Jr. and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.

This book 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.

Clifford Algebras And Spinor Structures

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Author : Rafal Ablamowicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Clifford Algebras And Spinor Structures written by Rafal Ablamowicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

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.

From Spinors To Supersymmetry

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Author :
language : en
Publisher: Cambridge University Press
Release Date :

From Spinors To Supersymmetry written by and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Theory Of Spinors And Its Application In Physics And Mechanics

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Author : Vladimir A. Zhelnorovich
language : en
Publisher: Springer Nature
Release Date : 2019-10-24

Theory Of Spinors And Its Application In Physics And Mechanics written by Vladimir A. Zhelnorovich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-24 with Science categories.

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.

From Spinors To Supersymmetry

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Author : Herbi K. Dreiner
language : en
Publisher: Cambridge University Press
Release Date : 2023-06-08

From Spinors To Supersymmetry written by Herbi K. Dreiner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-08 with Science categories.

Supersymmetry is an extension of the successful Standard Model of particle physics; it relies on the principle that fermions and bosons are related by a symmetry, leading to an elegant predictive structure for quantum field theory. This textbook provides a comprehensive and pedagogical introduction to supersymmetry and spinor techniques in quantum field theory. By utilising the two-component spinor formalism for fermions, the authors provide many examples of practical calculations relevant for collider physics signatures, anomalies, and radiative corrections. They present in detail the component field and superspace formulations of supersymmetry and explore related concepts, including the theory of extended Higgs sectors, models of grand unification, and the origin of neutrino masses. Numerous exercises are provided at the end of each chapter. Aimed at graduate students and researchers, this volume provides a clear and unified treatment of theoretical concepts that are at the frontiers of high energy particle physics.

Lie Groups And Algebras With Applications To Physics Geometry And Mechanics

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Author : D.H. Sattinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Lie Groups And Algebras With Applications To Physics Geometry And Mechanics written by D.H. Sattinger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.

This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselvesto the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.

Clifford Algebras And Spinors

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Author : Pertti Lounesto
language : en
Publisher: Cambridge University Press
Release Date : 2001-05-03

Clifford Algebras And Spinors written by Pertti Lounesto and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-03 with Mathematics categories.

In this book, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. The initial chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This book also gives the first comprehensive survey of recent research on Clifford algebras. A new classification of spinors is introduced, based on bilinear covariants of physical observables. This reveals a new class of spinors, residing between the Weyl, Majorana and Dirac spinors. Scalar products of spinors are classified by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the analytic side, Brauer-Wall groups and Witt rings are discussed, and Caucy's integral formula is generalized to higher dimensions.

The Theory Of Spinors

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Author : Elie Cartan
language : en
Publisher: Courier Corporation
Release Date : 1981-02-01

The Theory Of Spinors written by Elie Cartan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-02-01 with Mathematics categories.

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.

A Geometrical Approach To Physics

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Author : David A. Burton
language : en
Publisher: CRC Press
Release Date : 2024-03-20

A Geometrical Approach To Physics written by David A. Burton and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-20 with Mathematics categories.

This book provides an accessible introduction to using the tools of differential geometry to tackle a wide range of topics in physics, with the concepts developed through numerous examples to help the reader become familiar with the techniques. Physical applications are used to develop the techniques and demonstrate their wide-ranging applicability. Formalism is introduced sparingly and step-by-step, where it is needed, and chapters contain exercises for readers to test their understanding. Worked solutions to the exercises are included. It is an ideal textbook for advanced undergraduate or postgraduate courses on mathematical methods for physicists, for students whose background is in physics rather than mathematics. It is assumed that the reader has no prior knowledge of mathematical methods beyond the content of a standard undergraduate physics degree. The purpose of the book is to act as a ‘gateway’ to more advanced books on the applications of differential geometry in physics. It will also help the reader to better appreciate modern physics research that makes use of differential geometry, and the common features that permeate the discipline as a whole. Key Features: Presents a light and accessible treatment Can be used as a textbook for a short course on mathematical methods for physicists Accessible to advanced undergraduates and postgraduates whose background is in physics, not mathematics