Spinors In Physics

Invented by Dirac in creating his relativistic quantum theory of the electron, spinors are important in quantum theory, relativity, nuclear physics, atomic and molecular physics, and condensed matter physics. Essentially, they are the mathematical entities that correspond to electrons in the same way that ordinary wave functions correspond to classical particles. Because of their relations to the rotation group SO(n) and the unitary group SU(n), this discussion will be of interest to applied mathematicians as well as physicists.

Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities.

This conference brought together physicists and mathematicians working on spinors, which have played an important role in recent research on supersymmetry, Kaluza-Klein theories, twistors and general relativity. Contents:Killing Spinors According to O Hijazi and Applications (A Lichnerowicz)Self-Duality Conditions Satisfied by the Spin Connections on Spheres (J Rawnsley)Maslov Index and Half-Forms (M Cahen)Spin-3/2 Field on Black Hole Spacetimes (P Aichelburg)Indecomposable Conformal Spinors and Operator Product Expansions in a Massless QED Model (Y S Stanev & I T Todorov)Nonlinear Spinor Representations (R Raçka)Nonlinear Wave Equations for Intrinsic Spinor Coordinates (P Furlan)Twistors-“Spinors” of SU(2,2), Their Generalizations and Achievements (J Niederle)Spinors, Reflections and Clifford Algebras: A Review (R Coquereaux)SL (n,R) Spinors for Particles, Gravity and Superstrings (Dj Šijački)Spinors on Compact Riemann Surfaces (C Reina)Simple Spinors as Urfelder (E Caianiello)Applications of Cartan Spinors to Differential Geometry in Higher Dimensions (L P Hughston)Killing Spinors on Spheres and Projective Spaces (S Gutt)Spinor Structures on Homogeneous Riemann Spaces (L Dabroswki & A Trautman)Classical Strings and Minimal Surfaces (H Urbantke)Representing Spinors with Differential Forms (I M Benn & R W Tucker)Inequalities for Spinors Norms in Clifford Algebras (G N Hile & P Lounesto)The Importance of Spin (A O Barut)The Theory of World Spinors (Y Ne'eman) Readership: Theoretical physicists and mathematicians.

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.

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.

In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant methods may be used to elucidate the structure and properties of space-time. In volume 1, Two-spinor calculus and relativistic fields, the calculus of 2-spinors is introduced and developed. Volume 2, Spinor and twistor methods in space-time geometry, introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. This work will be of great value to all those studying relativity, differential geometry, particle physics and quantum field theory from beginning graduate students to experts in these fields.

There is now a greater range of mathematics used in theoretical physics than ever. The aim of this book is to introduce theoretical physicists, of graduate student level upwards, to the methods of differential geometry and Clifford algebras in classical field theory. Recent developments in particle physics have elevated the notion of spinor fields to considerable prominence, so that many new ideas require considerable knowledge of their properties and expertise in their manipulation. It is also widely appreciated now that differential geometry has an important role to play in unification schemes which include gravity. All the important prerequisite results of group theory, linear algebra, real and complex vector spaces are discussed. Spinors are approached from the viewpoint of Clifford algebras. This gives a systematic way of studying their properties in all dimensions and signatures. Importance is also placed on making contact with the traditional component oriented approach. The basic ideas of differential geometry are introduced emphasising tensor, rather than component, methods. Spinor fields are introduced naturally in the context of Clifford bundles. Spinor field equations on manifolds are introduced together with the global implications their solutions have on the underlying geometry. Many mathematical concepts are illustrated using field theoretical descriptions of the Maxwell, Dirac and Rarita-Schwinger equations, their symmetries and couplings to Einsteinian gravity. The core of the book contains material which is applicable to physics. After a discussion of the Newtonian dynamics of particles, the importance of Lorentzian geometry is motivated by Maxwell's theory of electromagnetism. A description of gravitation is motivated by Maxwell's theory of electromagnetism. A description of gravitation in terms of the curvature of a pseudo-Riemannian spacetime is used to incorporate gravitational interactions into the language of classical field theory. This book will be of great interest to postgraduate students in theoretical physics, and to mathematicians interested in applications of differential geometry in physics.

"...The aim of this book is to introduce theoretical physicists, of graduate student level upwards, to the methods of differential geometry and Clifford algebras in classical field theory..."--back cover.