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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.
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.
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
Spinors in Finite-Dimensional Euclidean Spaces.- Spinor Fields in a Riemannian Space.- Spinors in the Four-Dimensional Pseudo-Euclidean Space.- Spinors in Three-Dimensional Euclidean Spaces.- Tensor Forms of Differential Spinor Equations.- Exact Solutions of the Nonlinear Spinor Equations.- A. Relativistic Models of Spin Fluids in Electromagnetic Field.- B. Proper Bases and Invariant Internal Energy in the Theory of Electromagnetic Field.- C. The Bilinear Identities Connecting the Dirac Matrices.- Bibliography
| Erscheinungsjahr: | 2019 |
|---|---|
| Fachbereich: | Theoretische Physik |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Physik, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
xvi
392 S. |
| ISBN-13: | 9783030278359 |
| ISBN-10: | 3030278352 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Zhelnorovich, Vladimir A. |
| Auflage: | 1st edition 2019 |
| Hersteller: | Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 241 x 160 x 28 mm |
| Von/Mit: | Vladimir A. Zhelnorovich |
| Erscheinungsdatum: | 06.11.2019 |
| Gewicht: | 0,776 kg |
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
Spinors in Finite-Dimensional Euclidean Spaces.- Spinor Fields in a Riemannian Space.- Spinors in the Four-Dimensional Pseudo-Euclidean Space.- Spinors in Three-Dimensional Euclidean Spaces.- Tensor Forms of Differential Spinor Equations.- Exact Solutions of the Nonlinear Spinor Equations.- A. Relativistic Models of Spin Fluids in Electromagnetic Field.- B. Proper Bases and Invariant Internal Energy in the Theory of Electromagnetic Field.- C. The Bilinear Identities Connecting the Dirac Matrices.- Bibliography
| Erscheinungsjahr: | 2019 |
|---|---|
| Fachbereich: | Theoretische Physik |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Physik, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
xvi
392 S. |
| ISBN-13: | 9783030278359 |
| ISBN-10: | 3030278352 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Zhelnorovich, Vladimir A. |
| Auflage: | 1st edition 2019 |
| Hersteller: | Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 241 x 160 x 28 mm |
| Von/Mit: | Vladimir A. Zhelnorovich |
| Erscheinungsdatum: | 06.11.2019 |
| Gewicht: | 0,776 kg |
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