Lecture Notes in Physics
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Lecture Notes in Physics Edited by J. Ehlers, Mtinchen, K. Hepp, Ztirich R. Kippenhahn, Mtinchen, H. A. Weidenmiiller, Heidelberg and J. Zittartz, Kdln Managing Editor: W. Beiglbdck, Heidelberg 135 Group Theoretical Methods in Physics Proceedings of the IX International Colloquium Held at Cocoyoc, Mkxico, June 23-27,198O Edited by Kurt Bernard0 Wolf Sprirlger-Verlag Berlin Heidelberg New York 1980 Editor Kurt Bernard0 Wolf lnstituto de lnvestigaciones en Matematicas Aplicadas y en Sistemas (IIMAS) Universidad National Authoma de MBxico M6xico 20, D.F. ISBN 3-540-10271-X Springer-Verlag Berlin Heidelberg New York ISBN 0-387-10271-X Springer-Verlag NewYork Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of Illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under 5 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. 0 by Springer-Verlag Berlin Heidelberg 1980 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2153/3140-543210 Preface The importance which group theoretical methods have been acqui- ring in physics and the new mathematical developments in their track have made it increasingly necessary to have periodic conferences in this field. Thus in the early seventies, thanks to the efforts of members of the C}~RS in Marseille and of the University of Nijmegen, the Colloquia on Group Theoretical Hethods in Physics were started. Since then they have taken place regularly in '72 and '74 in Marseille, '73 and '75 in Nijmegen, '76 in Hontrdal, '77 in T~bingen, '78 in Aus- tin, and '79 in Kiriat Anavim, Israel. The IX International Colloquium on Group Theoretical Methods in Physics took place in Cocoyoc, an old hacienda converted into a re- sort and convention hotel, about 70 kilometers south of Mexico City, in the week of June 23 to 27, 1980. There were 121 participants from 22 countries who presented 15 invited talks and 93 contributed papers. The local organizing committee consisted of: Marcos Hoshinsky (Chairman) Clicerio Avilez Laurence Jacobs Charles P. Boyer Jerzy Pleba~ski Elpidio Chac6n Kurt Bernardo Wolf. Technical assistance was provided by Oscar Tronceso, with the coopera- tion of Beatriz Aizen, Armando Antill6n, Enrique Henestroza, Gustavo L6pez,and Socorro del Olmo. The members of the Standing Committee of the Group Theory Collo- quia are: H. Bacry, L. C. Biedenharn, J. L. Birman, K. Bleuler, A. Bohm, L. L. Boyle, A. P. Cracknell, G. G. Emch, L. P. Horwitz, A. Janner, B. R. Judd, P. Kramer, V. I. Man'ko, L. Hichel, M. Hoshinsky, Y. Ne'eman, C. Piron, S. Sternberg, P. Winternitz, and J. A. Wolf. IV The local organizing conunittee hopes that the atmQsphere in Coco- yoc was conducive to strong interactions between the participants. In fact, it seemed that some of the more interesting discussions on physics and mathematics occurred, besides in the lecture rooms, in the outside bar and around the swimming pool. The Colloquium was made possible thanks to the cooperation and financial assistance of the following institutions: INTERNATIONAL UNION OF PURE AND APPLIED PHYSICS UNIVERSIDAD NACIONAL AUTONOMA DE MEXICO CONSEJO NACIONAL DE CIENCIA Y TECNOLOGIA INSTITUTe NACIONAL DE INVESTIGACIONES NUCLEARES CENTRe DE INVESTIGACION Y ESTUDIOS AVANZADOS, IPN FOMENTO EDUCACIONAL A. C. To all of them the local committee wishes to express its gratitude. We are also indebted to the participants for their cooperation and pa- tience, and to the members of the Standing Committee who gave very help- ful advice. Marcos Moshinsky (Chairman, Local Organizing Committee) The local organizing committee for the IX Colloquium made a call for papers from the scientific community working with the appli- cations of group theoretical methods in physics, and invited some of the leading representatives of each field to deliver survey or impor- tant research talks. The program was set up giving one-hour plenary sessions to the invited speakers and half-hour simultaneous sessions to the contributed talks. No papers were rejected by the committee. Simultaneous sessions were held in order to accomodate the num- ber of presentations, dividing the papers into nine areas, in the way followed in these Proceedings. Care was taken so that a minimum of overlap should occur between talks delivered simultaneously. During the Conference, a Poster Session was created so as to accomodate for last-minute contributions, and for speakers who felt this was a better mode of interaction with their colleagues. In these Proceedings, all contributions -including invited speakers- are divided into the nine areas, and an author index is appended at the end. A high point in the IX Colloquium was the 1980 Wigner Medal ceremony, honouring Professor Izrail l~oiseevich Gel'fand. As Profes- sor Gel'fand could not receive the medal in person, a congratulatory telegram was signed by most of the participants. A Section on the Wigner Medal award is included in these Proceedings. OUR LOGO Early in the activities of the local organizing committee, we decided upon a logo which summarized a Mexican image in a group theoretical way: The duality between Life and Death as a broken symmetry. In the Totonac culture of the Atlantic coast there are a number of sculptures which depict a human face, one of whose halves shows the living person, and the other half his mask of death. Our logo was composed out of the two profiles and the front of one particularly beautifUl clay figure, some 12 by 15 cm, belonging to Dr. Kurt Stavenhagen. His private collection of prehispanic art is among the finest in Mexico, and he graciously allowed us to use it for the Colloquium poster - printed in purple and Mexican pink. C~ .H N 0 0 L~ 0 U .H 'H 0 ,-.-I ,-"f 0 U M I-.-t g4 0 m r~ Q~ r~ .,-I 4~ r~ LIST OF PARTICIPANTS V. AMAR C.P. BOYER Istituto di Fisica IIMAS-UNAM Universit~ di Parma Apdo. Postal 20-726 Parma, Italy M6xico 20, D.F., M6xico R.L. ANDERSON A.J. BRACKEN Dept. of Physics & Astronomy Dept. of Physics & Astrophysics University of Georgia University of Colorado Athens, Ga. 30602, USA Boulder, Colo. 80309, USA B. ANGEI~ANN J. BROECKHOVE Institut for Theoretische Physik Dienst Theoretische eu der Universit~t Clausthal Wiskundige Natuurkunde Clausthal, West Germany University of Antwerpen B-2020 Antwerpen, Belgium A. ANTILLON Instituto de Ffsica, UNA~[ P.H. BUTLER Apdo. Postal 20-364 Department of Physics M6xico 20, D.F., M~xico University of Canterbury Christchurch i, New Zealand J. AZCARRAGA Departamento de Ffsica Te6rica J.F. CARI~ENA Facultad de Ciencias F~sicas Departamento de Fisica Te6rica Burjasot, Valencia, Spain Facultad de Ciencias Universidad de Zaragoza I. BARS Zaragoza, Spain Physics Department Yale University O. CASTAFTOS New Haven, Conn. 06520, USA Centro de Estudios Nucleares, UN~{ Apdo. Postal 70-543 A.O. BARUT M@xico 20, D.F., ~i6xico Physics Department University of Colorado J.A. CASTILHO ALCARAS Boulder, Colo. 80309, USA Instituto de Ffsica Te6rica Rua Pamplona, 145 - CEP 01405 M. BERRONDO Sao Paulo, Brasil Instituto de Ffsica, UNAM Apdo. Postal 20-364 E. CHACON M6xico 20, D.F., M6xico Instituto de F~sica, UN~[ Apdo. Postal 20-364 L.C. BIEDENHARN M6xico 20, D.F., M6xico Department of Physics Duke University J.-O., CHEN Durham,N.C. 27706, USA Department of Physics Nanjing University A.M. BINCER Nanjing, People's Rep. of China Physics Department University of Wisconsin M. COUTURE Madison, Wis. 53706, USA Physics Department McGill University A. BOHM Montr6al, Qu6bec, Canada Center for Particle Theory University of Texas Austin, Texas 78712, USA A.P. CRACKNELL Carnegie Laboratory of Physics University of Dundee L.J. BOYA Dundee DDI 4HN, Scotland, U.K. Departamento de Fisica Te6rica Universidad de Salamanca Salamanca, Spain IX B.J. DALTON N. GIOVANNINI Department of Physics D6partement de Physique Th6orique Ames Laboratory Universit6 de Gen~v~ Iowa State University 121 Gen~ve 4, Switzerland Ames, Iowa 50011, USA S. GITLER E. DEUMENS CINVESTAV Dienst Theoretische eu Institute Polit6cnico Nacional Wiskundige Natuurkunde M6xico 14, D. F., M6xic0 University of Antwerpen B-2020 Antwerpen, Belgium R. GLEISER IMAF A. DIN Universidad de C6rdoba C.E.R.N. - TH C6rdoba, Argentina CH-1211 Gen~ve 23, Switzerland J.C.H. GODDARD R. DIRL Departamento de Matem~ticas Institut f~r Theoretische Physik Universidad Aut6noma Metropolitana Technische Universit~t Wien M6xico 14, D. F., M6xico~ A-1040 Wien, Austria V. GORINI J.P. DRAAYER Istituto di Fisica Department of Physics Universit~ di Milano Louisiana State University Milano, Italy Baton Rouge, La. 70803, USA M. GOTAY H. ECKSTEIN Department of Mathematics Centre de Physique Th6orique II University of Calgary F-13288 Marseille, Cedex 2, France Calgary T2N IN4, Canada F.J. ERNST A. GROSSMANN Physics Department Centre de Physique Th6orique II Illinois Institute of Technology F-13288 Marseille, Cedex 2, France Chicago, Ill. 60616, USA Z. HABA D. FELD~N Institute of Theoretical Physics Department of Physics University of Wroc~aw Brown University 50-205 Wroc~aw, Poland Providence, R.I. 02912, USA M. H~E~ESH F. GALLONE Department of Physics Istitute di Fisica A. Pontremoli University of Minnesota Via Celoria 16 Mineapolis, Minn. 55455, USA Milano 20133, Italy J. HARNAD A. GARCIA C~ CINVESTAV Universit~ de Montr@al Institute Polit6cnico Nacional C.P. 6128 M~xico 14, D. F., M~xico Montr6al, Qu@bec, Canada J.P. GAZEAU I. HAUSER Laboratoire de Chimie Physique Physics Department Universit6 Pierre et Marie Curie Lewis College of Sciences ii, rue Pierre et Marie Curie and Letters, IIT 75 231 Paris Cedex 05, France Chicago, Ill.