Spinor Structures in Geometry and Physics

Viktor Mikaylovich Red’kov (Editor)
Institute of Physics, Minsk, Belarus

Olga Vladimirovna Veko (Editor)
Republic of Belarus, Mozyr State Pedagogical University, Physical Department

Elena Mikhaylovna Ovsiyuk (Editor)
Mozyr State Pedagogical University, Belarus

Alexandru Oana (Editor)
University Transilvania of Brasov, Department of Algebra, Geometry and Differential Equations

Mircea Neagu (Editor)
University Transilvania of Brasov, Department of Algebra, Geometry and Differential Equations

Vladimir Balan (Editor)
University Politehnica of Bucharest

Series: Physics Research and Technology
BISAC: SCI074000

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This book is devoted to investigating the spinor structures in particle physics and in polarization optics. In fact, it consists of two parts joined by the question: Which are the manifestations of spinor structures in different branches of physics. It is based on original research. The main idea is the statement that the physical understanding of geometry should be based on physical field theories. The book contains numerous topics with the accent on field theory, quantum mechanics and polarization optics of the light, and on the spinor approach. (Imprint: Nova)

Introduction

1. Introductory Remarks

2. On the Geometry of Spaces and Spinor Structure

3. Spinor Structure. Kustaanheimo–Stiefel and Hopf Bundles

4. The Spin Covering for the Full Lorentz Group and the Concept of Fermion
Parity

5. Spinor Space Structure and Solutions of Klein–Fock–Gordon Equation

6. Fermion in Riemannian Space-Time

7. Polarization Optics and 2-Spinors

8. Polarization Optics and 4-spinors

9. Transitivity for the Lorentz Group and Polarization Optics

10. Parameters of Lorentz Matrices and Transitivity in Polarization Optics

11. Factorizations for 3-Rotations and the Polarization of the Light

12. On the Determining of Mueller Matrices from Polarization Measurements

13. Elementary Constituents of the Group SL(4,R) and Mueller Matrices

14. Degenerate 4-Dimensional Matrices with Semi-Group Structure

15. Degenerate Mueller Matrices, Semigroups and Projective Geometry

16. Diagonalization of Quadratic Forms and the Mueller Formalism

17. Finsler-Type Structures and Det-Based Classification of Mueller manifolds

Bibliography

Index

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