Fr. 83.00

Geometric Multivector Analysis - From Grassmann to Dirac

Englisch · Taschenbuch

Versand in der Regel in 1 bis 2 Wochen (Titel wird auf Bestellung gedruckt)

Beschreibung

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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.

 

Inhaltsverzeichnis

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.

Über den Autor / die Autorin










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.


Bericht

"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)

Produktdetails

Autoren Andreas Rosén
Verlag Springer, Berlin
 
Sprache Englisch
Produktform Taschenbuch
Erschienen 04.12.2020
 
EAN 9783030314132
ISBN 978-3-0-3031413-2
Seiten 465
Abmessung 157 mm x 26 mm x 236 mm
Illustration XIII, 465 p. 29 illus., 8 illus. in color.
Serie Birkhäuser Advanced Texts Basler Lehrbücher
Thema Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Arithmetik, Algebra

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