Geometric Methods in Physics

1. Front Matter

   Pages i-ix

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2. Higher Structures and Non-commutative Geometry

   1. Front Matter

      Pages 1-1

      PDF

   2. Traces of Holomorphic Families of Operators on the Noncommutative Torus and on Hilbert Modules

      • Sara Azzali, Cyril Lévy, Carolina Neira-Jiménez, Sylvie Paycha

      Pages 3-38

   3. r _∞-Matrices, Triangular L _∞-Bialgebras and Quantum_∞ Groups

      • Denis Bashkirov, Alexander A. Voronov

      Pages 39-47

   4. Normal Forms and Lie Groupoid Theory

      • Rui Loja Fernandes

      Pages 49-66

   5. Higher Braces Via Formal (Non)Commutative Geometry

      • Martin Markl

      Pages 67-81

   6. Conformally Rescaled Noncommutative Geometries

      • Andrzej Sitarz

      Pages 83-100

3. Quantum Mechanics and Field Theory

   1. Front Matter

      Pages 101-101

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   2. On Some Quaternionic Coherent States and Wavelets

      • S. Twareque Ali

      Pages 103-111

   3. Supersymmetric Vector Coherent States for Systems with Zeeman Coupling and Spin-Orbit Interactions

      • I. Aremua, E. Baloïtcha, M. N. Hounkonnou

      Pages 113-126

   4. Energy and Stability of the Pais–Uhlenbeck Oscillator

      • D. S. Kaparulin, S. L. Lyakhovich

      Pages 127-134

   5. Deformation Quantization with Separation of Variables and Gauge Theories

      • Yoshiaki Maeda, Akifumi Sako, Toshiya Suzuki, Hiroshi Umetsu

      Pages 135-144

   6. Physics of Spectral Singularities

      • Ali Mostafazadeh

      Pages 145-165

   7. On the Moduli Space of Yang–Mills Fields on \( \mathbb{R}^4 \)

      • Armen Sergeev

      Pages 167-176

   8. On Covariant Poisson Brackets in Field Theory

      • A. A. Sharapov

      Pages 177-186

4. Groups and Algebras

   1. Front Matter

      Pages 187-187

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   2. Weyl Group Orbit Functions in Image Processing

      • Goce Chadzitaskos, Lenka Háková, Ondřej Kajínek

      Pages 189-194

   3. Poisson and Fourier Transforms for Tensor Products and an Overalgebra

      • Vladimir F. Molchanov

      Pages 195-203

   4. Unipotent Flow on \( \text{SL}_2 \left( {\Bbb Z} \right)\backslash \text{SL}_2 \left( {\mathbb{R}} \right) \): From Dynamics to Elementary Number Theory

      • Nikolay Moshchevitin

      Pages 205-211

   5. Lie Superalgebras of Krichever–Novikov Type

      • Martin Schlichenmaier

      Pages 213-226

​This book presents a selection of papers based on the XXXIII Białowieża Workshop on Geometric Methods in Physics, 2014. The Białowieża Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Białowieża Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Białowieża forest in eastern Poland.

The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and mathematmtics.

• Lie groupoids and algebroids
• Poisson and non-commutative geometry
• integrable systems
• mathematical physics
• quantization

• Departamento de Física, CINVESTAV, Mexico City, Mexico

  Piotr Kielanowski

• Université Catholique de Louvain IRMP, Louvain-la-Neuve, France

  Pierre Bieliavsky

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

  Anatol Odzijewicz

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

  Martin Schlichenmaier

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

  Theodore Voronov

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