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Theory of Spinors and Its Application in Physics and Mechanics

  • 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)

  1. Front Matter

    Pages i-xvi
  2. Spinors in Finite-Dimensional Euclidean Spaces

    • Vladimir A. Zhelnorovich
    Pages 1-85
  3. Spinor Fields in a Riemannian Space

    • Vladimir A. Zhelnorovich
    Pages 87-115
  4. Spinors in the Four-Dimensional Pseudo-Euclidean Space

    • Vladimir A. Zhelnorovich
    Pages 117-202
  5. Spinors in Three-Dimensional Euclidean Spaces

    • Vladimir A. Zhelnorovich
    Pages 203-225
  6. Tensor Forms of Differential Spinor Equations

    • Vladimir A. Zhelnorovich
    Pages 227-288
  7. Exact Solutions of the Nonlinear Spinor Equations

    • Vladimir A. Zhelnorovich
    Pages 289-342
  8. Back Matter

    Pages 343-392

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

  • Institute of Mechanics, Moscow State University, Moscow, Russia

    Vladimir A. Zhelnorovich

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

Buy it now

Buying options

eBook USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access