Mielnik’s 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 well as the intricacies of the quantum time operator.

The Białowieża 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 (1931–1980) on the occasion of his 80th anniversary as well as on Bogdan Mielnik and Stanisław Lech Woronowicz on the occasion of their 75th and 70th birthdays, respectively. The groundbreaking work of Berezin is discussed from today’s 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 Stanisław Lech Woronowicz. Mielnik’s 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.

Mathematically precise discussion of the physical topics Concise description of the geometry of quantum states with relation to quantum entanglement and quantum computing Overview of the recent state of the interaction of geometry with modern physics Contributions of leading scientists in the field Documentation of Felix A. Berezin’s work and personal recollections by his former students and collaborators Includes supplementary material: sn.pub/extras