Ebook: Geometric Methods in Physics: XXX Workshop, Białowieża, Poland, June 26 to July 2, 2011

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 interchange ideas. This volume contains contributions by selected speakers at the XXX meeting in 2011 as well as additional review articles and shows that the workshop remains at the cutting edge of ongoing research.

The 2011 workshop focussed 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 their 75th and 70th birthday, 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, among other fields, active in representation theory, general concepts of quantization and coherent states, supersymmetry and supermanifolds.

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 well as 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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The Bia?owie?a 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 Stanis?aw 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 Stanis?aw 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.

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The Bia?owie?a 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 Stanis?aw 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 Stanis?aw 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-xix
Front Matter....Pages 1-1
Felix Alexandrovich Berezin and His Work....Pages 3-33
Some Non-standard Examples of Coherent States and Quantization....Pages 35-42
Classical and Quantum Evolution on the Siegel-Jacobi Manifolds....Pages 43-52
Exhausting Formal Quantization Procedures....Pages 53-62
On One Result of F. Berezin....Pages 63-69
Berezin Quantization on Para-Hermitian Symmetric Spaces....Pages 71-80
Remarks on Singular Symplectic Reduction and Quantization of the Angular Moment....Pages 81-89
Duality and the Abel Map for Complex Supercurves....Pages 91-99
Berezin’s Coherent States, Symbols and Transform for Compact K?hler Manifolds....Pages 101-116
Physically Acceptable Solutions of an Eigenvalue Equation in Deformation Quantization....Pages 117-123
A Classification Theorem and a Spectral Sequence for a Locally Free Sheaf Cohomology of a Supermanifold....Pages 125-132
Front Matter....Pages 133-133
Bogdan Mielnik: Contributions to Quantum Control....Pages 135-156
Partial Inner Product Spaces, a Unifying Language for Quantum Mechanics....Pages 157-164
The Resonance-Decay Problem in Quantum Mechanics....Pages 165-174
Geometry of the Set of Mixed Quantum States: An Apophatic Approach....Pages 175-197
Solution Hierarchies for the Painlev? IV Equation....Pages 199-209
The Marvelous Consequences of Hardy Spaces in Quantum Physics....Pages 211-228
Factorization Method and the Position-dependent Mass Problem....Pages 229-237
Quantum Configuration Spaces of Extended Objects, Diffeomorphism Group Representations and Exotic Statistics....Pages 239-251
Convex Geometry: A Travel to the Limits of Our Knowledge....Pages 253-264
Front Matter....Pages 133-133
A Time of Arrival Operator on the Circle (Variations on Two Ideas)....Pages 265-274
Negative Time Delay for Wave Reflection from a One-dimensional Semi-harmonic Well....Pages 275-281
Front Matter....Pages 283-283
Characterizing Non-Markovian Dynamics....Pages 285-293
Deformation Quantization of a Harmonic Oscillator in a General Non-commutative Phase Space: Energy Spectrum in Relevant Representations....Pages 295-302
Front Matter....Pages 303-310
Pencils of Conics as a Classification Code....Pages 311-311
Geodesic Mappings and Einstein Spaces....Pages 313-322
Racah Operators....Pages 323-330
Pseudopotentials via Moutard Transformations and Differential Geometry....Pages 331-335
Proving the Jacobi Identity the Hard Way....Pages 337-341
L?wner-Kufarev Evolution in the Segal-Wilson Grassmannian....Pages 343-348
The pre-Maxwell Equations....Pages 349-356
Serret’s Curves, their Generalization and Explicit Parametrizations....Pages 357-366
Harmonic Spheres Conjecture....Pages 367-376
Lax Equations and the Knizhnik–Zamolodchikov Connection....Pages 377-381
Short-time Asymptotics for Semigroups of Diffusion Type and Beyond....Pages 383-390
Front Matter....Pages 391-404
Bureaucratic World: Is it Unavoidable?....Pages 405-413
....Pages 415-422