Geometric Methods in Physics (eBook)

Preface.- Part I: Higher Structures and Non-commutative Geometry.- S. Azzali, C. Lévy, C. Neira-Jiménez and S. Paycha: Traces of Holomorphic Families of Operators on the Noncommutative Torus and on Hilbert Modules.- D. Bashkirov and A. Voronov: r∞- Matrices, Triangular L∞- Bialgebras, and Quantum∞ Groups.- R. Fernandes: Normal Forms and Lie Groupoid Theory.- M. Markl: Higher Braces via Formal (Non)commutative Geometry.- A. Sitarz: Conformally Rescaled Noncommutative Geometries.- Part II: Quantm Mechanics and Field Theory.- S. Twareque Ali: On Some Quaternionic Coherent States and Wavelets.- I. Aremua, E. Baloïtcha and M. N. Hounkonnou: Supersymmetric Vector Coherent States for Systems with Zeeman Coupling and Spin-orbit Interactions.- D.S. Kaparulin and S.L. Lyakhovich: Energy and Stability of Pais-Uhlenbeck Oscillator.- Yoshiaki Maeda, Akifumi Sako, Toshiya Suzuki and Hiroshi Umetsu: Deformation Quantization with Separation of Variables and Gauge Theories.- Ali Mostafazadeh: Physics of Spectral Singularities.- Armen Sergeev: On the Moduli Space of Yang-Mills Fields on ℝ^4.- A. A. Sharapov: On Covariant Poisson Brackets in Field Theory.- Part III: Groups and Algebras.- G. Chadzitaskos, L. Háková and O. Kajínek: Weyl Group Orbit Functions in Image Processing.- V.F. Molchanov: Poisson and Fourier Transforms for Tensor Products and an Overalgebra.- N. Moshchevitin: Unipotent Flow on SL2(ℤ)/SL2(ℝ): from Dynamics to Elementary Number Theory.- Martin Schlichenmaier: Lie Superalgebras of Krichever-Novikov Type.- E.G. Vishnyakova: On n-ary Lie algebras of type (r; l).- Part IV: Integrable Systems and Special Functions.- A. Dobrogowska and G. Jakimowicz: The class of (q; h) –Hahn Orthogonal Polynomials.- A. Dobrogowska and T. Goliński: Examples of Hamiltonian Systems on the Space of Deformed Skew-symmetric Matrices.- Y. A. Neretin: Matrix Beta-integrals: an Overview.- A. Savin and B. Sternin: Differential Equations on Complex Manifolds.- E. Schmeidel, J. Zonenberg and B. Łupińska: Asymptotic Properties of Solutions of Neutral Type Difference System with Delays.- E. Shemyakova: Orbits of Darboux Groupoid for Hyperbolic Operators of Order Three.- Part V: Special Economic Session.- B. Mielnik: From Nicolaus Copernicus Economical Law up to the Present Day Economic Disasters.- Ł. Hardt: Economics – Physics of Social Sciences or Art?.