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

432 Pages·1993·13.73 MB·English

by  Jan Rzewuski (auth.)

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