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Algebra --- 51 <082.1> --- Mathematics--Series --- Spinor analysis. --- Analyse spinorielle. --- Spinor analysis --- Calculus of spinors --- Spinor calculus --- Spinors, Theory of --- Wave mechanics --- Calculus of tensors --- Vector analysis

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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.

General relativity (Physics) --- Spinor analysis. --- Calculus of spinors --- Spinor calculus --- Spinors, Theory of --- Algebra --- Wave mechanics --- Calculus of tensors --- Vector analysis --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics --- Relativity (Physics)

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This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry. After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index. Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.

Spinor analysis. --- Clifford algebras. --- Geometric algebras --- Algebras, Linear --- Calculus of spinors --- Spinor calculus --- Spinors, Theory of --- Algebra --- Wave mechanics --- Calculus of tensors --- Vector analysis --- Geometry. --- Group theory. --- Mathematical physics. --- Group Theory and Generalizations. --- Mathematical Methods in Physics. --- Physical mathematics --- Physics --- Groups, Theory of --- Substitutions (Mathematics) --- Mathematics --- Euclid's Elements --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.

Spinor analysis. --- Space and time. --- Geometry, Differential. --- Mathematical physics. --- Physical mathematics --- Physics --- Differential geometry --- Space of more than three dimensions --- Space-time --- Space-time continuum --- Space-times --- Spacetime --- Time and space --- Fourth dimension --- Infinite --- Metaphysics --- Philosophy --- Space sciences --- Time --- Beginning --- Hyperspace --- Relativity (Physics) --- Calculus of spinors --- Spinor calculus --- Spinors, Theory of --- Algebra --- Wave mechanics --- Calculus of tensors --- Vector analysis --- Mathematics

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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.

Spinor analysis. --- Calculus of spinors --- Spinor calculus --- Spinors, Theory of --- Algebra --- Wave mechanics --- Calculus of tensors --- Vector analysis --- Physics. --- Elementary particles (Physics). --- Quantum field theory. --- Cosmology. --- Mathematical physics. --- Algebraic geometry. --- Mathematical Methods in Physics. --- Elementary Particles, Quantum Field Theory. --- Mathematical Physics. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Physical mathematics --- Physics --- Astronomy --- Deism --- Metaphysics --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Mathematics