Geometric Multivector Analysis - Andreas Rosén

Geometric Multivector Analysis

From Grassmann to Dirac

(Autor)

Buch | Softcover
XIII, 465 Seiten
2020 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-31413-2 (ISBN)
64,19 inkl. MwSt

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 20th-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.

 

lt;p>Andreas Rosén is a Professor at the Chalmers University of Technology and the University of Gothenburg, Sweden. His research mostly concerns Partial Differential Equations, and uses techniques from harmonic analysis and operator theory.

Prelude: Linear algebra.- Exterior algebra.- Clifford algebra.- Mappings of inner product spaces.- Spinors in inner product spaces.- Interlude: Analysis.- Exterior calculus.- Hodge decompositions.- Hypercomplex analysis.- Dirac equations.- Multivector calculus on manifolds.- Two index theorems.

"The book is carefully prepared and well presented, and I recommend the book ... for students who have just mastered vector calculus and Maxwellian electromagnetism." (Hirokazu Nishimura, zbMATH 1433.58001, 2020)

Erscheinungsdatum
Reihe/Serie Birkhäuser Advanced Texts Basler Lehrbücher
Zusatzinfo XIII, 465 p. 29 illus., 8 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 730 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Schlagworte boundary value problems, • Clifford Algebra • Dirac Equations • Exterior algebra • Hodge decompositions • index theorems • matrix theory • Partial differential equations • spinors
ISBN-10 3-030-31413-8 / 3030314138
ISBN-13 978-3-030-31413-2 / 9783030314132
Zustand Neuware
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