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.

Zusammenfassung
The papers in this volume are devoted to quantum group theory, non-commutative differential geometry and integrable systems. Emphasis is given to the formalism of noncommutative geometry on the quantum geometry of quantum groups and the quantum deformation of Poincare algebra.

Inhalt

Section I: Quantum Groups. 1. Sugawara Construction and the Q-Deformation of Virasoro Algebra; M. Chaichian, P. Presnajder. 2. Complex Quantum Groups and Their Dual Hopf Algebras; B. Drabant, M. Schlieker, W. Weich, B. Zumino. 3. Extremal Projector and Universal R-matrix for Quantized Contragredient Lie (Super)Algebras; S.M. Khoroshkin, V.N. Tolstoy. 4. Quantum Deformations of D=4 Poincaré Algebra; J. Lukierski, A. Nowicki. 5. Quantum Group' Structure and Covariant' Differential Calculus on Symmetric Algebras Corresponding to Commutation Factors on Zn; R. Matthes. 6. Remarks on the Use of R-Matrices; A. Schirrmacher. 7. Construction of Some Hopf Algebras; E. Sorace. 8. Realifications of Complex Quantum Groups; S. Zakrzewski. Section II: Non Commutative Differential Geometry. 1. On Multigraded Differential Calculus; A. Borowiec, W. Marcinek, Z. Oziewicz. 2. Yang Mills Fields and Symmetry Breaking: From Lie Super-Algebras to Non Commutative Geometry; R. Coquereaux. 3. Differential and Integral Calculus on the Quantum C-Plane; J. Rembielinski. Section III: Integrable Systems. 1. Rigorous Approach to Abelian Chern-Simons Theory; S. Albeverio, J. Schäfer. 2. The Conformal Block Structure of Perturbation Theory in Two Dimensions; R. Flume. 3. An Alternative Dynamical Description of Quantum Systems; B. Fuchssteiner. 4. On the Solutions of the Yang-Baxter Equations; L. Hlavatý. 5. State Sum Invariants of Compact 3-Manifolds with Boundary and 6j-Symbols; M. Karowski, W. Müller, R. Schrader. Section IV: Miscellaneous. 1. Product of States; K. Fredenhagen. 2. Quantum Measurements and Information Theory; K.-E. Hellwig. 3. A Comment on a 3-Dimensional Euclidean Supersymmetry; J. Łopuszánski. 4. Chiral Nets and Modular Methods; B. Schroer. 5. Chiral Symmetry Breaking -- Rigorous Results; M. Salmhofer, E. Seiler. 6. On a Twister Shift in Particle and String Dynamics; V.A. Soroka, D.P. Sorokin, V.I. Tkach, D.V. Volkov. 7. The Metric of Bures and the Heometric Phase; A. Uhlmann.