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Geometric Methods in Physics

XXX Workshop, Białowieża, Poland, June 26 to July 2, 2011

  • Conference proceedings
  • © 2013

Overview

Editors:
  1. Piotr Kielanowski

    1. Departamento de Física, CINVESTAV, Mexico City, Mexico

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  2. S. Twareque Ali

    1. Dept. of Mathematics and Statistics, Concordia University, Montreal, Canada

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  3. Anatol Odzijewicz

    1. Institute of Mathematics, University of Bialystok, Bialystok, Poland

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  4. Martin Schlichenmaier

    1. Mathematics Research Unit, FSTC, University of Luxembourg, Luxembourg-Kirchberg, Luxembourg

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  5. Theodore Voronov

    1. School of Mathematics, University of Manchester, Manchester, United Kingdom

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  • 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

Part of the book series: Trends in Mathematics (TM)

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Table of contents (39 papers)

  1. Front Matter

    Pages i-xix
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  2. Quantization, Supergeometry and Representation Theory, the Scientific Legacy of Felix A. Berezin

    1. Front Matter

      Pages 1-1
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    2. Felix Alexandrovich Berezin and His Work

      • Alexander Karabegov, Yuri Neretin, Theodore Voronov
      Pages 3-33

    3. Some Non-standard Examples of Coherent States and Quantization

      • S. Twareque Ali
      Pages 35-42

    4. Classical and Quantum Evolution on the Siegel-Jacobi Manifolds

      • Stefan Berceanu
      Pages 43-52

    5. Exhausting Formal Quantization Procedures

      • Vasily A. Dolgushev
      Pages 53-62

    6. On One Result of F. Berezin

      • Simon Gindikin
      Pages 63-69

    7. Berezin Quantization on Para-Hermitian Symmetric Spaces

      • Vladimir F. Molchanov
      Pages 71-80

    8. Remarks on Singular Symplectic Reduction and Quantization of the Angular Moment

      • V. P. Palamodov
      Pages 81-89

    9. Duality and the Abel Map for Complex Supercurves

      • Jeffrey M. Rabin
      Pages 91-99

    10. Berezin’s Coherent States, Symbols and Transform for Compact Kähler Manifolds

      • Martin Schlichenmaier
      Pages 101-116

    11. Physically Acceptable Solutions of an Eigenvalue Equation in Deformation Quantization

      • Jaromir Tosiek
      Pages 117-123

    12. A Classification Theorem and a Spectral Sequence for a Locally Free Sheaf Cohomology of a Supermanifold

      • E. G. Vishnyakova
      Pages 125-132

  3. Foundations of Quantum Mechanics

    1. Front Matter

      Pages 133-133
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    2. Bogdan Mielnik: Contributions to Quantum Control

      • David J. Fernández C.
      Pages 135-156

    3. Partial Inner Product Spaces, a Unifying Language for Quantum Mechanics

      • Jean-Pierre Antoine
      Pages 157-164

    4. The Resonance-Decay Problem in Quantum Mechanics

      • Hellmut Baumgärtel
      Pages 165-174

    5. Geometry of the Set of Mixed Quantum States: An Apophatic Approach

      • Ingemar Bengtsson, Stephan Weis, Karol Życzkowski
      Pages 175-197

    6. Solution Hierarchies for the Painlevé IV Equation

      • David Bermúdez, David J. Fernández C.
      Pages 199-209

    7. The Marvelous Consequences of Hardy Spaces in Quantum Physics

      • Arno Bohm, Hai Viet Bui
      Pages 211-228
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Keywords

About this book

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.

Editors and Affiliations

  • Departamento de Física, CINVESTAV, Mexico City, Mexico

    Piotr Kielanowski

  • Dept. of Mathematics and Statistics, Concordia University, Montreal, Canada

    S. Twareque Ali

  • Institute of Mathematics, University of Bialystok, Bialystok, Poland

    Anatol Odzijewicz

  • Mathematics Research Unit, FSTC, University of Luxembourg, Luxembourg-Kirchberg, Luxembourg

    Martin Schlichenmaier

  • School of Mathematics, University of Manchester, Manchester, United Kingdom

    Theodore Voronov

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