Geometric Multivector Analysis From Grassmann to Dirac /

• Main Author: Rosén, Andreas (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2019.
• Edition: 1st ed. 2019.
• Series: Birkhäuser Advanced Texts Basler Lehrbücher,
• Subjects: Matrix theory.; Algebra.; Global analysis (Mathematics).; Manifolds (Mathematics).; Partial differential equations.; Integral equations.; Differential geometry.; Linear and Multilinear Algebras, Matrix Theory.; Global Analysis and Analysis on Manifolds.; Partial Differential Equations.; Integral Equations.; Differential Geometry.

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...

Table of Contents:

• 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.