Ebook: Groups and Related Topics: Proceedings of the First Max Born Symposium

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.

---

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 Poincar? 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.

---

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 Poincar? 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.

Content:
Front Matter....Pages i-viii
Front Matter....Pages 1-1
Sugawara Construction and the Q-Deformation of Virasoro Algebra....Pages 3-12
Complex Quantum Groups and Their Dual Hopf Algebras....Pages 13-22
Extremal projector and universal R-matrix for quantized contragredient Lie (super)algebras....Pages 23-32
Quantum Deformations of D = 4 Poincar? Algebra....Pages 33-44
Remarks on the Use of R-matrices....Pages 45-54
Construction of Some Hopf Algebras....Pages 55-65
Realifications of complex quantum groups....Pages 67-81
Front Matter....Pages 83-100
On Multigraded Differential Calculus....Pages 101-101
Yang Mills fields and symmetry breaking: From Lie super-algebras to non commutative geometry....Pages 103-114
Differential and Integral Calculus on the Quantum C-Plane....Pages 115-127
Front Matter....Pages 129-139
Rigorous Approach to Abelian Chern-Simons Theory....Pages 141-141
The Conformal Block Structure of Perturbation Theory in Two Dimensions....Pages 143-152
An alternative dynamical description of Quantum Systems....Pages 153-163
On the solutions of the Yang-Baxter equations....Pages 165-178
State sum invariants of compact 3-manifolds with boundary and 6j-symbols....Pages 179-188
Front Matter....Pages 189-196
Product of States....Pages 197-197
Quantum Measurements and Information Theory....Pages 199-209
A Comment on a 3-Dimensional Euclidean Supersymmetry....Pages 211-221
Chiral Nets And Modular Methods....Pages 223-231
Front Matter....Pages 233-245
Chiral Symmetry Breaking — Rigorous Results....Pages 197-197
On a twistor shift in particle and string dynamics....Pages 247-257
The Metric of Bures and the Geometric Phase....Pages 259-266
Back Matter....Pages 267-274
....Pages 275-275