Spinors, Twistors, Clifford Algebras and Quantum Deformations: Proceedings of the Second Max Born Symposium held near Wrocław, Poland, September 1992 PDF
Preview Spinors, Twistors, Clifford Algebras and Quantum Deformations: Proceedings of the Second Max Born Symposium held near Wrocław, Poland, September 1992
Spinors, Twistors, Clifford Algebras and Quantum Deformations Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN V AN DER MERWE University of Denver, USA Editorial Advisory Board: ASIM BARUT, University of Colorado , US.A. BRIAN D, JOSEPHSON, University of Cambridge, UK. CLIVE KILMISTER, University of London, UK. GUNTER LUDWIG, Philipps-Universittit, Marburg, Germany NATHAN ROSEN, Israel Institute of Technology, Israel MENDEL SACHS, State University of New York at Buffalo, US.A. ABDUS SALAM, International Centre for Theoretical Physics, Trieste, Italy HANS-JURGEN TREDER, Zentralinstitutfur Astrophysik der Akademie der Wissenschaften, Germany Volume 52 Spinors, Twistors, Clifford Algebras and Quantum Deformations Proceedings of the Second Max Born Symposium held near Wroclaw, Poland, September 1992 edited by Zbigniew Oziewicz Bernard Jancewicz and Andrzej Borowiec Institute of Theoretical Physics, University ofWroclaw, Wroclaw, Poland SPRINGER SCIENCE+BUSINESS MEDIA,B.V. Library of Congress Cataloging-in-Publication Data Sp,nars, tWlstars, Cllffard algebras, and quantum defarmatlans edlted by Zblgnlew OZleW1CZ, Bernard JanceW1CZ, and AndrzeJ BaraWlec. p. cm. -- (Fundamental thearles of phYS1CS v. 52) ISBN 978-94-010-4753-1 ISBN 978-94-011-1719-7 (eBook) DOI 10.1007/978-94-011-1719-7 1. Splnor analysls--Congresses. 2. TWlstar theary--Congresses. 3. Cllffard algebras--Congresses .. 4. Mathematlcal phYS1CS- -Cangresses. 5. Rzewuskl, Jan, 1916- I. OZlewlcz, Zblgnlew. II. Jancewlcz. Bernard. III. Barawlec, AndrzeJ, 1950- IV. Ser les. aC20.7.S65S67 1993 530.1'5257--dc20 93-7413 ISBN 978-94-010-4753-1 Printed on acid-free paper AH Rights Reserved © 1993 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1993 Softcover reprint ofthe hardcover Ist edition 1993 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. This volume is dedicated to Professor Jan Rzewuski) pioneer and teacher) on the occasion of his 75-th birthday TABLE OF CONTENTS Foreword Zbigniew Oziewicz xiii Photograph of Professor Jan Rzewuski XIX Homage to Professor Jan Rzewuski Jan Lopuszariski xxi Homage to Professor Jan Rzewuski Jan Mozrzymas xxiii Photograph of participants xxiv SPINORS Structure of matrix manifolds and a particle model Jan Rzewuski 3 Complex stuctures and the Elie Cartan approach to the theory of spinors Michel Dubois-Violette 17 Spin structures on hypersurfaces and the spectrum of the Dirac operator on spheres A ndrzej Trautman 25 Algebraic construction of spin structures on homogeneous spaces Vladimir Lyakhovsky 31 The Kummer configuration and the geometry of Majorana spinors Gary W. Gibbons 39 viii TABLE OF CONTENTS Pauli-Kofink identities and pure spinors Helmut Urbantke 53 General covariance and spinors Ludwik Dgbrowski 61 Tensored division algebras: origin of geometry, spinors and symmetry Geoffrey Dixon 67 G-Structure for hypermanifolds Andrzej Borowiec 75 Towards a unification of "everything" with gravity Jerzy Rayski 81 Generalized Fierz identitites and the superselection rule for geometric multispinors William M. Pezzaglia, jr. 91 Electrons, photons and spinors in the Pauli algebra William Baylis 97 TWISTORS Twistors and supersymmetry Dmitrij Volkov 109 A twistor-like description of D=10 superstrings and D=l1 supermembranes Igor Bandos and Aleksandr Zheltukhin 121 Born's reciprocity in the conformal domain Arkadiusz Jadczyk 129 Self-dual Einstein supermanifolds and supertwistor theory Sergey Merkulov 141 An approach to the construction of coherent states for massless particles Andrzej Karpio 147 TABLE OF CONTENTS ix CLIFFORD ALGEBRAS What is a bivector ? Pertti Lounesto 153 Monogenic forms on manifolds Vladimir Soucek 159 On invertibility of the Clifford algebra elements with disjoint supports Pavel Semenov 167 Clifford algebras and algebraic structure of fundamental fermions Wojciech Krolikowski 171 Clifford algebra of two-forms, conformal structures and field equations Ingemar Bengtsson 183 Dirac form of Maxwell equation; ~n-graded algebras Jaime Keller 189 Travelling waves within the Clifford algebra Bernard Jancewicz 197 Hamiltonian mechanics with geometric calculus David Hestenes 203 Grassmann mechanics, multivector derivatives and geometric algebra Chris Doran, Anthony Lasenby and Steve Gull 215 Intrinsic non-invariant forms of Dirac equation Josep Manel Parra 227 2-spinors, twistors and supersymmetry in the space-time algebra Anthony Laseby, Chris Doran and Steve Gull 233 x TABLE OF CONTENTS QUANTUM DEFORMATIONS Quantized Minkowski space Julius Wess, Bruno Zumino, Oleg Ogievetsky and W.B. Schmidke 249 = D 4 Quantum Poincare algebra and finite difference time deri'Vative Jerzy Lukierski, Anatol Nowicki and Henri Ruegg 257 Quantum Lorentz group and q-deformed Clifford algebra Ursula Carow-Watamura 267 Isotropic q-Lorentz group Jakub Rembielinski 277 Lorentz algebra and twists Ralf Engeldinger, Michael Schlieker and Wolfgang Weich 281 On a noncommutative extension of electrodynamics John Madore 285 Bicovariant differential calculus and q-deformation of gauge theory Satoshi Watamum 299 Cyclic paragrassmann representations for covariant quantum algebras Alexey Isaev 309 Hecke symmetries and braided Lie algebras Dmitri Gurevich 317 Anyonic quantum groups Shahn Majid 327 On S-Lie-Cartan pairs Wladyslaw Marcinek 337 New real forms of Uq(G) kn&k~ ~ TABLE OF CONTENTS xi RELATED TOPICS ~3-graded structures Richard Kerner 349 On Jordan block form Garret Sobczyk 357 Unified theory of spin and angular momentum Leopold Halpern 365 Noetherian symmetries in particle mechanics and classical field theory Dan Grigore 371 Lienard-Wiechert Yang-Mills fields I<. Paul Tod 379 The twist prescription in the topological Yang-Mills theory Sorin Marculescu 391 On symmetry properties of classical Lagrange functions under rotations Peter Stichel and Jan Lopuszmiski 403 Tunnelling of neutral particle with spin 1/2 through magnetic field Mijat Mijatovic, G. Ivanovski, B. Veljanoski and G. Apostolovska 413 List of participants 421
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