An introduction to spinors and geometry with applications in by Ian M. Benn, Robin W. Tucker

By Ian M. Benn, Robin W. Tucker

There's now a better variety of arithmetic utilized in theoretical physics than ever. the purpose of this ebook is to introduce theoretical physicists, of graduate pupil point upwards, to the tools of differential geometry and Clifford algebras in classical box idea. fresh advancements in particle physics have increased the suggestion of spinor fields to significant prominence, in order that many new principles require significant wisdom in their houses and services of their manipulation. it's also commonly liked now that differential geometry has a huge position to play in unification schemes which come with gravity. the entire vital prerequisite result of workforce thought, linear algebra, actual and intricate vector areas are mentioned. Spinors are approached from the point of view of Clifford algebras. this offers a scientific approach of learning their houses in all dimensions and signatures. value can also be put on making touch with the conventional part orientated technique. the fundamental principles of differential geometry are brought emphasising tensor, instead of part, equipment. Spinor fields are brought clearly within the context of Clifford bundles. Spinor box equations on manifolds are brought including the worldwide implications their recommendations have at the underlying geometry. Many mathematical strategies are illustrated utilizing box theoretical descriptions of the Maxwell, Dirac and Rarita-Schwinger equations, their symmetries and couplings to Einsteinian gravity. The center of the publication comprises fabric that's appropriate to physics. After a dialogue of the Newtonian dynamics of debris, the significance of Lorentzian geometry is stimulated via Maxwell's concept of electromagnetism. an outline of gravitation is inspired by way of Maxwell's conception of electromagnetism. an outline of gravitation by way of the curvature of a pseudo-Riemannian spacetime is used to include gravitational interactions into the language of classical box thought. This publication might be of serious curiosity to postgraduate scholars in theoretical physics, and to mathematicians drawn to functions of differential geometry in physics.

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