Spinors, Twistors, Clifford Algebras and Quantum Deformations : Proceedings of the Second Max Born Symposium Held Near Wrocław, Poland, September 1992

ZBIGNIEW OZIEWICZ University of Wroclaw, Poland December 1992 The First Max Born Symposium in Theoretical and Mathematical Phy­ sics, organized by the University of Wrodaw, was held in September 1991 with the intent that it would become an annual event. It is the outgrowth of the annual Seminars organized jointly since 1972 with the University of Leipzig. The name of the Symposia was proposed by Professor Jan Lopu­ szanski. Max Born, an outstanding German theoretical physicist, was born in 1883 in Breslau (the German name of Wrodaw) and educated here. The Second Max Born Symposium was held during the four days 24- 27 September 1992 in an old Sobotka Castle 30 km west of Wrodaw. The Sobotka Castle was built in the eleventh century. The dates engraved on the walls of the Castle are 1024, 1140, and at the last rebuilding, 1885. The castle served as a cloister until the end of the sixteenth century. Front Matter....Pages i-xxv Front Matter....Pages 1-1 Structure of Matrix Manifolds and a Particle Model....Pages 3-16 Complex Structures and the Elie Cartan Approach to the Theory of Spinors....Pages 17-23 Spin Structures on Hypersurfaces and the Spectrum of the Dirac Operator on Spheres....Pages 25-29 Algebraic Construction of Spin Structures on Homogeneous Spaces....Pages 31-38 The Kummer Configuration and the Geometry of Majorana Spinors....Pages 39-52 Pauli-Kofink Identities and Pure Spinors....Pages 53-60 General Covariance and Spinors....Pages 61-65 Tensored Division Algebras: Origin of Geometry, Spinors and Symmetry....Pages 67-74 G — Structure for Hypermanifold....Pages 75-79 Towards a Unification of ”Everything” with Gravity....Pages 81-89 Generalized Fierz Identities and the Superselection Rule for Geometric Multispinors....Pages 91-96 Electrons, Photons, and Spinors in the Pauli Algebra....Pages 97-106 Front Matter....Pages 107-107 Twistors and Supersymmetry....Pages 109-119 A Twistor-Like Description of D = 10 Superstrings and D = 11 Supermembranes....Pages 121-127 Born’s Reciprocity in the Conformal Domain....Pages 129-140 Self-Dual Einstein Supermanifolds and Supertwistor Theory....Pages 141-146 An Approach to the Construction of Coherent States for Massless Particles....Pages 147-150 Front Matter....Pages 151-151 What is a Bivector?....Pages 153-158 Monogenic Forms on Manifolds....Pages 159-166 On Invertibility of Clifford Algebras Elements with Disjoint Supports....Pages 167-169 Front Matter....Pages 151-151 Clifford Algebras and Algebraic Structure of Fundamental Fermions....Pages 171-181 Clifford Algebra of Two-Forms, Conformal Structures, and Field Equations....Pages 183-188 Dirac form of Maxwell Equation Z n -Graded Algebras....Pages 189-196 Travelling Waves within the Clifford Algebra....Pages 197-201 Hamiltonian Mechanics with Geometric Calculus....Pages 203-214 Grassmann Mechanics, Multivector Derivatives and Geometric Algebra....Pages 215-226 Intrinsic Non-Invariant Forms of Dirac Equation....Pages 227-232 2-Spinors, Twistors and Supersymmetry in the Spacetime Algebras....Pages 233-245 Front Matter....Pages 247-247 Quantized Minkowski Space....Pages 249-256 D = 4 Quantum Poincaré Algebras and Finite Difference Time Derivatives....Pages 257-266 Quantum Lorentz Group and q -Deformed Clifford Algebra....Pages 267-276 Isotropic q -Lorentz Group....Pages 277-279 Lorentz Algebra and Twists....Pages 281-284 On a Noncommutative Extension of Electrodynamics....Pages 285-298 Bicovariant Differential Calculus and q -Deformation of Gauge Theory....Pages 299-308 Cyclic Paragrassmann Representations for Covariant Quantum Algebras....Pages 309-316 Hecke Symmetries and Braided Lie Algebras....Pages 317-326 Anyonic Quantum Groups....Pages 327-336 On S -Lie-Cartan Pairs....Pages 337-342 New Real Forms of U q ( G )....Pages 343-346 Front Matter....Pages 347-347 Z 3 -Graded Structures....Pages 349-356 Jordan Form in Associative Algebras....Pages 357-364 Unified Theory of Spin and Angular Momentum....Pages 365-370 Noetherian Symmetries in Particle Mechanics and Classical Field Theory....Pages 371-377 Liénard-Wiechert Yang-Mills Fields....Pages 379-389 The Twist Prescription in the Topological Yang-Mills Theory....Pages 391-401 On Symmetry Properties of Certain Classical Lagrange Functions under Rotations....Pages 403-412 Tunnelling of Neutral Particle with Spin 1/2 through Magnetic Field....Pages 413-420 Back Matter....Pages 421-430 This volume contains the lectures given at the Second Max Born Symposium held near Wroclaw in Poland in September 1992. The various authoritative contributions provide an excellent review of recent developments in the field and embrace the following topics: spin structures; the interrelations between Cartan's and Chevalley's theory of spinors, Clifford algebras and particle models; the interrelations between twistors, supersymmetry and phase spaces; quantum deformations; noncommutative Hopf algebras; noncommutative calculus and its applications in electrodynamics and in gauge theory; and deformed Clifford algebras and Z3-graded algebras. For researchers and graduate students in mathematical and theoretical physics.