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Birkhäuser Advanced Texts Basler Lehrbücher

Geometric Multivector Analysis

From Grassmann to Dirac

Authors: Rosén, Andreas

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  • Develops carefully the foundations of calculus of multivector fields and differential forms
  • Explains advanced material in a self-contained and down-to-earth way, e.g. Clifford algebra, spinors, differential forms and index theorems
  • Touches on modern research areas in analysis
  • Contains a novel treatment of Hodge decompositions based on first-order differential operators
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eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-030-31411-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
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Hardcover $99.99
price for USA in USD
  • ISBN 978-3-030-31410-1
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  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

 

About the authors

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.

Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-030-31411-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.99
price for USA in USD
  • ISBN 978-3-030-31410-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Multivector Analysis
Book Subtitle
From Grassmann to Dirac
Authors
Series Title
Birkhäuser Advanced Texts Basler Lehrbücher
Copyright
2019
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-31411-8
DOI
10.1007/978-3-030-31411-8
Hardcover ISBN
978-3-030-31410-1
Series ISSN
1019-6242
Edition Number
1
Number of Pages
XIII, 465
Number of Illustrations
21 b/w illustrations, 8 illustrations in colour
Topics