Clifford Algebras and Their Applications in Mathematical Physics

Front Matter....Pages i-xix
A Unified Language for Mathematics and Physics....Pages 1-23
Clifford Algebras and Spinors....Pages 25-37
Pseudo-Euclidean Hurwitz Pairs and Generalized Fueter Equations....Pages 39-48
A New Representation for Spinors in Real Clifford Algebras....Pages 49-60
Primitive Idempotents and Indecomposable Left Ideals in Degenerate Clifford Algebras....Pages 61-65
Groupes De Clifford Et Groupes Des Spineurs....Pages 67-78
Spin Groups Associated with Degenerate Orthogonal Spaces....Pages 79-91
Algebres De Clifford Separables II....Pages 93-102
Sur Une Question De Micali-Villamayor....Pages 103-107
Spingroups and Spherical Monogenics....Pages 109-114
Left Regular Polynomials in Even Dimensions, and Tensor Products of Clifford Algebras....Pages 115-132
Spingroups and Spherical Means....Pages 133-147
The Biregular Functions of Clifford Analysis: Some Special Topics....Pages 149-158
Clifford Numbers and Möbius Transformations in R n ....Pages 159-166
A Clifford Calculus for Physical Field Theories....Pages 167-175
Generalized C-R Equations on Manifolds....Pages 177-199
Integral Formulae in Complex Clifford Analysis....Pages 201-217
Killing Vectors and Embedding of Exact Solutions in General Relativity....Pages 219-226
From Grassmann to Clifford....Pages 227-244
Lorentzian Applications of Pure Spinors....Pages 245-255
The Poincaré Group....Pages 257-263
Minimal Ideals and Clifford Algebras in the Phase Space Representation of Spin-1/2 Fields....Pages 265-272
Some Consequences of the Clifford Algebra Approach to Physics....Pages 273-283
Algebraic Ideas in Fundamental Physics from Dirac-Algebra to Superstrings....Pages 285-292
On two Supersymmetric Approaches to Quantum Gravity: Clifford Algebra Degeneracy v Extended Objects....Pages 293-312
Clifford Algebra and the Interpretation of Quantum Mechanics....Pages 313-320
Representation-Free Calculations in Relativistic Quantum Mechanics....Pages 321-346
Dirac Equation for Bispinor Densities....Pages 347-352
Unified Spin Gauge Theory Models....Pages 353-361
U(2,2) Spin-Gauge Theory Simplification by use of the Dirac Algebra....Pages 363-370
Spin(8) Gauge Field Theory....Pages 371-376
Clifford Algebras, Projective Representations and Classification of Fundamental Particles....Pages 377-383
Fermionic Clifford Algebras and Supersymmetry....Pages 385-391
On Geometry and Physics of Staggered Lattice Fermions....Pages 393-398
A System of Vectors and Spinors in Complex Spacetime and their Application to Elementary Particle Physics....Pages 399-423
Spinors as Components of the Metrical Tensor in 8-Dimensional Relativity....Pages 425-434
Multivector Solution to Harmonic Systems....Pages 435-443
The Importance of Meaningful Conservation Equations in Relativistic Quantum Mechanics for the Sources of Classical Fields....Pages 445-454
Electromagnetic Theory and Network Theory Using Clifford Algebra....Pages 455-463
Remarks on Clifford Algebra in Classical Electromagnetism....Pages 465-483
Quaternionic Formulation of Classical Electromagnetic Fields and Theory of Functions of a Biquaternion Variable....Pages 485-493
Comparison of Clifford and Grassmann Algebras in Applications to Electromagnetics....Pages 495-500
Symplectic Clifford Algebras....Pages 501-515
Walsh Functions, Clifford Algebras and Cayley-Dickson Process....Pages 517-529
Z(N)-Spin Systems and Generalised Clifford Algebras....Pages 531-540
Generalized Clifford Algebras and Spin Lattice Systems....Pages 541-548
Clifford Algebra, Its Generalisations and Physical Applications....Pages 549-554
Application of Clifford Algebras to *-Products....Pages 555-558
On Regular Functions of a Power-Associative Hypercomplex Variable....Pages 559-564
On a Geometric Torogonal Quantization Scheme....Pages 565-572
Back Matter....Pages 573-582
....Pages 583-592