Overview
- A pragmatic handbook on the most important spinor equations of field theory and quantum mechanics
- Covers the Einstein–Dirac equations, nonlinear Heisenberg's equations, and equations for relativistic spin fluids
- An accessible introduction to Cartan, which could become very important again in modern cosmology
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
- pseudo-Eucliedean spaces
- Riemannian spaces
- Einstein-Dirac equations
- spin fluids
- tensor representation of spinors
- spinor fields
- tensor fields
- Dirac matrices
- complex Euclidean spaces
- nonlinear Heisenberg equations
- Lorentz group
- tetrad formalism
- Minkowski space
- semi spinors
- Maxwell equations
- Fermi-Walker transport
- Gamma matrices
About this book
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 equationscontaining, 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.
Authors and Affiliations
Bibliographic Information
Book Title: Theory of Spinors and Its Application in Physics and Mechanics
Authors: Vladimir A. Zhelnorovich
DOI: https://doi.org/10.1007/978-3-030-27836-6
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-27835-9Published: 06 November 2019
Softcover ISBN: 978-3-030-27838-0Published: 06 November 2020
eBook ISBN: 978-3-030-27836-6Published: 24 October 2019
Edition Number: 1
Number of Pages: XVI, 392
Additional Information: This book is a revised and updated version of the original Russian edition “Theory of Spinors and its Application in Physics and Mechanics” published by Izdatel'stvo Nauka, Moscow, Russia, 1982
Topics: Mathematical Methods in Physics, Elementary Particles, Quantum Field Theory, Cosmology, Mathematical Physics, Algebraic Geometry