Geometric Methods in Physics [electronic resource] : XXX Workshop, Biaowieʭa, Poland, June 26 to July 2, 2011 / edited by Piotr Kielanowski, S. Twareque Ali, Anatol Odzijewicz, Martin Schlichenmaier, Theodore Voronov.

The Biaowieʭa workshops on Geometric Methods in Physics are among the most important meetings in the field. Every year, some 80 to 100 participants from both mathematics and physics join to discuss new developments and to exchange ideas. This volume includes contributions by selected speakers at the 30th meeting in 2011 as well as additional review articles and it shows that the workshop remains at the cutting edge of ongoing research. The 2011 meeting focused on the works of the late Felix A. Berezin (19311980) on the occasion of his 80th anniversary as well as on Bogdan Mielnik and Stanisaw Lech Woronowicz on the occasion of their 75th and 70th birthdays, respectively. The groundbreaking work of Berezin is discussed from todays perspective by presenting an overview of his ideas and their impact on further developments. He was active in representation theory, general concepts of quantization and coherent states, supersymmetry and supermanifolds, among other fields. Another focus lies on the accomplishments of Bogdan Mielnik and Stanisaw Lech Woronowicz. Mielniks geometric approach to the description of quantum mixed states, the method of quantum state manipulation and their important implications for quantum computing and quantum entanglement are discussed, as are the intricacies of the quantum time operator. Woronowicz fruitful notion of a compact quantum group and related topics are also addressed.

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