Geometric Methods in Physics: XXXII Workshop, Białowieża, Poland, June 30-July 6, 2013 (Trends in Mathematics)

The Białowieża Workshops on Geometric Methods in Physics, which are hosted in the unique setting of the Białowieża natural forest in Poland, are among the most important meetings in the field. Every year some 80 to 100 participants from both the mathematics and physics world join to discuss new developments and to exchange ideas. The current volume was produced on the occasion of the 32 nd meeting in 2013. It is now becoming a tradition that the Workshop is followed by a School on Geometry and Physics, which consists of advanced lectures for graduate students and young researchers. Selected speakers at the 2013 Workshop were asked to contribute to this book, and their work was supplemented by additional review articles. The selection shows that, despite its now long tradition, the workshop remains at the cutting edge of research. The 2013 Workshop also celebrated the 75 th birthday of Daniel Sternheimer, and on this occasion the discussion mainly focused on his contributions to mathematical physics such as deformation quantization, Poisson geometry, symplectic geometry and non-commutative differential geometry. 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. Content: Front Matter....Pages i-ix Front Matter....Pages 1-2 Daniel Sternheimer....Pages 3-5 “The Important Thing is not to Stop Questioning”, Including the Symmetries on Which is Based the Standard Model....Pages 7-37 Bargmann–Fock Realization of the Noncommutative Torus....Pages 39-48 Berezin Transform and a Deformation Decomposition....Pages 49-56 Toeplitz Quantization without Measure or Inner Product....Pages 57-66 States in Deformation Quantization....Pages 67-76 Front Matter....Pages 77-77 Quantum Mechanics and Geometry on the Siegel–Jacobi Disk....Pages 79-88 Quantum Resonances: Theory and Models....Pages 89-98 Front Matter....Pages 99-118 Symplectic Dual Pair Related to Deformed The Bialowieza Workshops on Geometric Methods in Physics, which are hosted in the unique setting of the Bialowieza natural forest in Poland, are among the most important meetings in the field.