Theory Of Spinors And Its Application In Physics And Mechanics
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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.
Theory Of Spinors And Its Application In Physics And Mechanics
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Author : Vladimir Arkadʹevich Zhelnorovich
language : en
Publisher:
Release Date : 2019
Theory Of Spinors And Its Application In Physics And Mechanics written by Vladimir Arkadʹevich Zhelnorovich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Spinor analysis 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 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.
Spinors In Physics
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Author : Jean Hladik
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Spinors In Physics written by Jean Hladik 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 2012-12-06 with Science categories.
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.
From Spinors To Quantum Mechanics
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Author : Gerrit Coddens
language : en
Publisher:
Release Date : 2015
From Spinors To Quantum Mechanics written by Gerrit Coddens and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Science categories.
From Spinors to Quantum Mechanics discusses group theory and its use in quantum mechanics. Chapters 1 to 4 offer an introduction to group theory, and it provides the reader with an exact and clear intuition of what a spinor is, showing that spinors are just a mathematically complete notation for group elements. Chapter 5 contains the first rigorous derivation of the Dirac equation from a simple set of assumptions. The remaining chapters will interest the advanced reader who is interested in the meaning of quantum mechanics. They propose a novel approach to the foundations of quantum mechanics, based on the idea that the meaning of the formalism is already provided by the mathematics. In the traditional approach to quantum mechanics as initiated by Heisenberg, one has to start from a number of experimental results and then derive a set of rules and calculations that reproduce the observed experimental results. In such an inductive approach the underlying assumptions are not given at the outset. The reader has to figure them out, and this has proven to be difficult. The book shows that a different, bottom-up approach to quantum mechanics is possible, which merits further investigation as it demonstrates that with the methods used, the reader can obtain the correct results in a context where one would hitherto not expect this to be possible.
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.
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.
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.
The Theory Of Spinors
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Author : Élie Cartan
language : en
Publisher: Courier Corporation
Release Date : 2012-04-30
The Theory Of Spinors written by Élie 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 2012-04-30 with Mathematics categories.
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 Spinors And Geometry With Applications In Physics
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Author : Ian M. Benn
language : en
Publisher:
Release Date : 1987
An Introduction To Spinors And Geometry With Applications In Physics written by Ian M. Benn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Introduction To 2 Spinors In General Relativity
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Author : Peter J O'donnell
language : en
Publisher: World Scientific
Release Date : 2003-04-03
Introduction To 2 Spinors In General Relativity written by Peter J O'donnell and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-03 with Science categories.
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.