Clifford Algebras and their Applications in Mathematical Physics: Volume 1: Algebra and Physics1 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. |
Contents
V | 3 |
VI | 21 |
VII | 39 |
VIII | 49 |
IX | 73 |
XI | 75 |
XII | 93 |
XIII | 101 |
XXII | 239 |
XXIV | 241 |
XXV | 265 |
XXVI | 279 |
XXVII | 299 |
XXVIII | 317 |
XXX | 319 |
XXXI | 337 |
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Clifford Algebras and Their Applications in Mathematical Physics: Algebra ... Rafał Abłamowicz No preview available - 2000 |
Common terms and phrases
antisymmetric automorphism B₁ B₂ basis elements bilinear form bivector bundle calculus classical Clifford algebra commutation connection construction corresponding covariant derivative Definition deformed denote differential forms dimension dimensional Dirac equation Dirac operator dual Euclidean example extensor field finite functions geometric algebra geometric product given Gp,q grade Hecke algebra hermitian Hestenes homogeneous Hopf algebra Hurwitz hyperbolic idempotents invariant isomorphism Kähler Lie algebra linear complex linear space logic Lorentz Lounesto manifold Math Mathematical matrix metric Minkowski module momentum multivectors non-commutative notation obtain octonionic orthogonal P₁ paravector particle Phys physics plane Poincaré polynomial projective Proof pseudotwistors q-deformed quadratic quantum field theory quantum group quaternal quaternionic relativistic representation represented result rotation scalar smooth form fields solutions spacetime spin spinor structure subspace symmetric tangent tensor Theorem tion transformation vector field vector space Young operators zero