Geometric Multivector Analysis : From Grassmann to Dirac. 1st ed. 2019

種類:

電子ブック

責任表示:

by Andreas Rosén

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2019

著者名:

• Rosén, Andreas.
• SpringerLink (Online service)

シリーズ名:

Birkhäuser Advanced Texts Basler Lehrbücher ;

ISBN:

9783030314118 [3030314111]    

注記:

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.
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

ローカル注記:

学内専用E-BOOKS (local access only)