Clifford Algebras and their Applications in Mathematical Physics, Vol.1: Algebra and Physics

Rafal Ablamowicz; Bertfried Fauser

ISBN 10: 0817641823 ISBN 13: 9780817641825

Verlag: Birkhäuser Boston, 2000

Sprache: Englisch

Zustand: Neu Hardcover

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Bibliografische Details

Titel

Clifford Algebras and their Applications in Mathematical Physics, Vol.1: Algebra and Physics

Verlag

Birkh�user Boston

Erscheinungsjahr

2000

Sprache

Englisch

ISBN-10

0817641823

ISBN-13

9780817641825

Einband

Hardcover

Zustand

New

Verk�uferkataloge

�ber diesen Titel

Inhaltsangabe

1 Physics - Applications and Models.- Multiparavector Subspaces of C?n: Theorems and Applications.- Quaternionic Spin.- Pauli Terms Must Be Absent in the Dirac Equation.- Electron Scattering in the Spacetime Algebra.- 2 Physics - Structures.- Twistor Approach to Relativistic Dynamics and to the Dirac Equation - A Review.- Fiber with Intrinsic Action on a 1 + 1 Dimensional Spacetime.- Dimensionally Democratic Calculus and Principles of Polydimensional Physics.- A Pythagorean Metric in Relativity.- Clifford-Valued Clifforms: A Geometric Language for Dirac Equations.- 3 Geometry and Logic.- The Principle of Duality in Clifford Algebra and Projective Geometry.- Doing Geometric Research with Clifford Algebra.- Clifford Algebra of Quantum Logic.- 4 Mathematics - Deformations.- Hecke Algebra Representations in Ideals Generated by q-Young Clifford Idempotents.- On q-Deformations of Clifford Algebras.- Dirac Operator, Hopf Algebra of Renormalization and Structure of Space-time.- Non-commutative Spaces for Graded Quantum Groups and Graded Clifford Algebras.- 5 Mathematics - Structures.- Clifford Algebras and the Construction of the Basic Spinor and Semi-Spinor Modules.- On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form.- Covariant Derivatives on Minkowski Manifolds.- An Introduction to Pseudotwistors: Spinor Solutions vs. Harmonic Forms and Cohomology Groups.- Ordinary Differential Equation: Symmetries and Last Multiplier.- Universal Similarity Factorization Equalities Over Complex.

Rese�a del editor

The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. This volume is devoted specifically to the mathematical aspects of Clifford algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, "q"-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.

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