In the seventies and eighties, scientific collaboration between the Theory Section of the Physics Department of Leipzig University and the Institute of Theoretical Physics of the University of Wroolaw was established. This manifested itself, among other things, in the organization of regular, twice-yearly seminars located alternatively in Wrodaw and Leipzig. These Seminars in Theoretical Physics took place 27 times, the last during November 1990. In order to continue the traditions of German-Polish contacts in theoretical physics, we decided to start a new series of Seminars in Theoretical Physics and name them after the outstanding German theoretical physicist Max Born who was born in 1883 in Wrodaw. We hope that these seminars will continue to contribute to better scientific contacts and understanding between German and Polish theoretical physicists. The First Max Born Symposium was held in Wojnowice Castle, 20 km west of Wrodaw, 27 - 29 September 1991. Wojnowice Castle was built in the 16th century by the noble Boner family, in the Renaissance style, and has been recently adapted as a small conference center. The preferred subjects at the Symposium were Quantum Groups and Integrable Models. The Symposium was organized by Doctors R. Gielerak and Z. Popowicz under the scientific supervision of the undersigned.

Klappentext

This volume presents the lectures given by distinguished contributors at the First German-Polish Max Born Symposium, held at Wojnowice in Poland in September, 1991. This is the first such symposium to continue the tradition of a German-Polish collaboration in theoretical physics in the form of biannual seminars organized between the Universities of Leipzig and Wroclaw since the early seventies. The papers in this volume are devoted to quantum group theory, noncommutative differential geometry, and integrable systems. Particular emphasis is given to the formalism of noncommutative geometry on quantum groups, the quantum deformation of Poincaré algebra and the axiomatic approach to superselection rules. Possible relations between noncommutative geometry and particle physics models are also considered. For researchers and postgraduate students of theoretical and mathematical physics.

Inhalt
Section I Quantum Groups.- Sugawara Construction and the Q-Deformation of Virasoro Algebra.- Complex Quantum Groups and Their Dual Hopf Algebras.- Extremal Projector and Universal R-matrix for Quantized Contragredient Lie (super)algebras.- Quantum Defonnations of D = 4 Poincaré Algebra.- Quantum Group Structure and Covariant Differential Calculus on Symmetric Algebras Corresponding to Commutation Factors on Zn.- Remarks on the Use of R-matrices.- Construction of Some Hopf Algebras.- Realifications of Complex Quantum Groups.- Section II Non Commutative Differential Geometry.- On Multigraded Differential Calculus.- Yang Mills Fields and Symmetry Breaking: From Lie Super-Algebras to Non Commutative Geometry.- Differential and Integral Calculus on the Quantum C-Plane.- Section III Integrable Systems.- Rigorous Approach to Abelian Chern-Simons Theory.- The Conformal Block Structure of Perturbation Theory in Two Dimensions.- An Alternative Dynamical Description of Quantum Systems.- On the Solutions of the Yang-Baxter Equations.- State Sum Invariants of Compact 3-Manifolds with Boundary and 6j-symbols.- Section IV Miscellaneous.- Product of States.- Quantum Measurements and Information Theory.- A Comment on a 3-Dimensional Euclidean Supersymmetry.- Chiral Nets and Modular Methods.- Chiral Symmetry Breaking - Rigorous Results.- On a Twistor Shift in Particle and String Dynamics.- The Metric of Bures and the Geometric Phase.