Clifford Algebras and Their Application in Mathematical Physics: Aachen 1996

458 Pages·1998·16.872 MB·English

by  Thomas Ackermann (auth.), Volker Dietrich, Klaus Habetha, Gerhard Jank (eds.)

Clifford Algebras and Their Application in Mathematical Phy
Fundamental Theories of Physics
An International Book Series on The Fundamental Theories of Physics:
Their Clarification, Development and Application
Editor:
Alwyn van der Merwe, University of Denver, U.S.A.
Editoral Advisory Board:
Lawrence P. Horwitz, Tel-Aviv University, Israel
Brian D. Josephson, University of Cambridge, U.K.
Clive Kilmister, University of London, U.K.
Pekka J. Lahti, University of Turku, Finland
Günter Ludwig, Philipps-Universität, Marburg, Germany
Asher Peres, Israel Institute of Technology, Israel
Nathan Rosen, Israel Institute of Technology, Israel
Eduard Prugovecki, University of Toronto, Canada
Mendel Sachs, State University of New York at Buffalo, U.S.A.
Abdus Salam, International Centre for Theoretical Physics, Trieste, Italy
Hans-Jürgen Treder, Zentralinstitut für Astrophysik der Akademie der Wissenschaften,
Germany
Volume 94
Clifford Algebras and
Their Application in
Mathematical Physics
Aachen 1996
edited by
Volker Dietrich
Klaus Habetha
and
Gerhard Jank
Department of Mathematics,
Rheinisch-Westfälischen Technischen Hochschule,
Aachen, Germany
SPRINGER SCIENCE+BUSINESS MEDIA, B.V.
A CLP. Catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-6114-8 ISBN 978-94-011-5036-1 (eBook)
DOI 10.1007/978-94-011-5036-1
Printed on acid-free paper
All Rights Reserved
©1998 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1998
Softcover reprint of the hardcover 1st edition 1998
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
TABLE OF CONTENTS
Preface Xl
Participants of the 4th Conference on Clifford Algebras Xlll
Program of the 4th Conference on Clifford algebras XXVll
Th. Ackermann,
Dirac Operators and Clifford Geometry - New Unifying
Principles in Particle Physics? ............................... 1
M.B. Balk and M.Ya. Mazalov,
On the Hayman uniqueness problem for poly harmonic
functions ................................................... 11
S. Bernstein,
Left-linear and Nonlinear Riemann problems in Clifford
analysis .................................................... 17
J. Bures,
Spin structures and harmonic spinors on nonhyperelliptic
Riemann surfaces of small genera ........................... 31
P. Cerejeiras,
Decomposition of analytic hyperbolically harmonic functions 45
J .S.R. Chisholm and R.S. Farwell,
Spin Gauge Theories: A Summary .......................... 53
J. Cnops,
Manifolds with and without embeddings .................... 57
C. Daviau,
Dirac equation in the Clifford algebra of Space .............. 67
B. Fauser,
Dirac theory from a field theoretic point of view ............. 89
K. Gurlebeck,
On some applications of the biharmonic eqllation .......... 109
VI
D. Hestenes,
Spinor Particle Mechanics ................................. 129
U. Kahler,
Clifford analysis and elliptic boundary vallie problems
in unbounded domains ..................................... 145
J. Keller,
Twistors and Clifford Algebras ............................. 161
V.V. Kisil,
How Many Essentialy Different Function Theories Exist? ... 17.5
W. Haussmann and 0.1. Kounchev,
Variational Property of the Peano Kernel for Harmonicity
Differences of Order p ..................................... 185
P. Van Lancker,
Clifford Analysis on the Sphere ............................ 201
J. Lawrynowicz,
Type-changing transformations of pseudo-Euclidean
Hurwitz pairs, Clifford Analysis, and particle lifetimes ...... 217
Th. Hempfling and H. Leutwiler,
Modified quaternionic analysis in JR4 ...................... 227
H. Li,
Geometric Algebra and Lobachevski Geometry ............. 239
H.R. Malonek,
Generalizing the (F,G)- derivative in the sense of Bers ..... 247
A. Micali,
Formes quadratiques de Hardy-Weinberg et algebres de
Clifford ................................................... 2.59
D. Miralles,
On Dirac equations in curved space-times .................. 267
E. Obolashvili,
Some Partial Differential Equations in Clifford Analysis .... 275
J.M. Parra,
Teaching Clifford Algebra as Physical ~1athematics ........ 291
W.M. Pezzaglia Jr.,
Polydimensional Relativity, a Classical Generalization of
the Automorphism Invariance Principle .................... 305
W.A. Rodrigues Jr. and J. Vaz Jr.,
Subluminal and Superluminal Electromagnetic Waves
and the Lepton Mass Spectrum ............................ 319
S. Somaroo,
Higher Spin and the Spacetime Algebra .................... 347
F. Sommen,
Curved Radon Transforms in Clifford Analysis ............. 369
VB
W. Sprossig,
On a class of non-linear boundary value problems .......... 383
M. Cahen, S. Gutt and A. Trautman,
Pin structures and the Dirac operator on real projective
spaces and quadrics ....................................... 391
J. Vaz Jr.,
Construction of monopoles and instantons by using
spinors and the inversion theorem .......................... 401
K.P. Wojciechowski, S.G. Scott, G. Morchio and B. Booss-Bavnbek,
Determinants, Manifolds with Boundary and
Dirac Operators ........................................... 423
R. Yamaleev,
New dynamical equations for many particl(' system
on the basis of multicomplex algebra ....................... 433

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