Geometric Multivector Analysis

Name: Geometric Multivector Analysis
Brand: Springer Nature Switzerland AG
SKU: 9783030314101
Price: 2012 CZK
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From Grassmann to Dirac

Autor: Andreas Rosén

Jazyk:

Vazba: Pevná

Vydavatel: Springer Nature Switzerland AG

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This book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focu...

Informace o knize

Autor

Andreas Rosén

Jazyk

Angličtina

Vazba

Kniha - Pevná

Vydáno

2019

Stránek

465

EAN

9783030314101

Enbook ID

24520052

Vydavatel

Springer Nature Switzerland AG

Hmotnost

881

Rozměry

155 x 235 x 32

Kompletní popis

This book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects. Following in the footsteps of M. Riesz and L. Ahlfors, the book also explains how Clifford algebra offers the ideal tool for studying spacetime isometries and Möbius maps in arbitrary dimensions. The book carefully develops the basic calculus of multivector fields and differential forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes's theorem as compared to standard literature. It touches on recent research areas in analysis and explains how the function spaces of multivector fields are split into complementary subspaces by the natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the analysis is done on bounded domains in Euclidean space, with a focus on analysis at the boundary. The book also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds, one of the most celebrated achievements of 20 th -century mathematics. The book is primarily intended for graduate and PhD students of mathematics. It is also recommended for more advanced undergraduate students, as well as researchers in mathematics interested in an introduction to geometric analysis.

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Geometric Multivector Analysis

From Grassmann to Dirac

Informace o knize

Kompletní popis

Mohlo by vás zajímat

Zákaznicí kteří koupili tuto knihu koupili také