Spinors, Twistors, Clifford Algebras and Quantum Deformations de Andrzej Borowiec

Spinors, Twistors, Clifford Algebras and Quantum Deformations

Andrzej Borowiec

Bernard Jancewicz

Zbigniew Oziewicz

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.

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Cuprins

Spinors.- Structure of matrix manifolds and a particle model.- Complex stuctures and the Elie Cartan approach to the theory of spinors.- Spin structures on hypersurfaces and the spectrum of the Dirac operator on spheres.- Algebraic construction of spin structures on homogeneous spaces.- The Kummer configuration and the geometry of Majorana spinors.- Pauli-Kofink identities and pure spinors.- General covariance and spinors.- Tensored division algebras: origin of geometry, spinors and symmetry.- G-Structure for hypermanifolds.- Towards a unification of “everything” with gravity.- Generalized Fierz identitites and the superselection rule for geometric multispinors.- Electrons, photons and spinors in the Pauli algebra.- Twistors.- Twistors and supersymmetry.- A twistor-like description of D=10 superstrings and D=11 supermembranes.- Born’s reciprocity in the conformal domain.- Self-dual Einstein supermanifolds and supertwistor theory.- An approach to the construction of coherent states for massless particles.- Clifford Algebras.- What is a bivector ?.- Monogenic forms on manifolds.- On invertibility of the Clifford algebra elements with disjoint supports.- Clifford algebras and algebraic structure of fundamental fermions.- Clifford algebra of two-forms, conformal structures and field equations.- Dirac form of Maxwell equation; ?n-graded algebras.- Travelling waves within the Clifford algebra.- Hamiltonian mechanics with geometric calculus.- Grassmann mechanics, multivector derivatives and geometric algebra.- Intrinsic non-invariant forms of Dirac equation.- 2-spinors, twistors and supersymmetry in the space-time algebra.- Quantum Deformations.- Quantized Minkowski space.- D = 4 Quantum Poincaré algebra and finite difference time derivative.- Quantum Lorentz groupand q-deformed Clifford algebra.- Isotropic q- Lorentz group.- Lorentz algebra and twists.- On a noncommutative extension of electrodynamics.- Bicovariant differential calculus and q-deformation of gauge theory.- Cyclic paragrassmann representations for covariant quantum algebras.- Hecke symmetries and braided Lie algebras.- Anyonic quantum groups.- On S-Lie-Cartan pairs.- New real forms of Uq(G).- Related Topics.- ?3-graded structures.- On Jordan block form.- Unified theory of spin and angular momentum.- Noetherian symmetries in particle mechanics and classical field theory.- Liénard-Wiechert Yang-Mills fields.- The twist prescription in the topological Yang-Mills theory.- On symmetry properties of classical Lagrange functions under rotations.- Tunnelling of neutral particle with spin 1/2 through magnetic field.- List of participants.