Geometric Methods in Physics XXXVI (eBook)

FM.- Part I:Quantum Mechanics and Mathematics – Twareque Ali in Memoriam.-In Memory of S. Twareque Ali.- Two-dimensional non commutative Swanson model and its bicoherent states.- Universal Markov kernels for quantum observables.-  Coherent states associated to the Jacobi group and Berezin quantization of the Siegel-Jacobi ball.- 1D & 2D Covariant affine integral quantizations.- Diffeomorphism group representations in relativistic quantum field theory.- Part II: Noncommutative Geometry.- Skew derivations on down-up algebras.- On noncommutative geometry of the Standard Model: fermion multiplet as internal forms.- Recursion operator in a noncommutative Minkowski phase space.- Decompactifying spectral triples.- Dirac operator on a noncommutative Toeplitz torus.- Part III: Quantization.- Field quantization in the presence of external fields.- Quantization of Mathematical Theory of Non-Smooth Strings.- The reasonable effctiveness of mathematical deformation theory in physics.- Axiomatic attempt at states in deformation quantisation.- Exact Lagrangian submanifolds and the moduli space of special Bohr-Sommerfeld Lagrangian cycles.- Star Exponentials in Star Product Algebra.- Part IV: Integrable Systems.- Beyond recursion operators.- Kepler Problem and Jordan Algebras.- On Rank Two Algebro-Geometric Solutions of an Integrable Chain.- Part V: Differential Geometry and Physics.- The Dressing Field Method of Gauge Symmetry Reduction: Presentation and Examples.- A differential model for B-type Landau-Ginzburg theories.- On the Dirac type operators on symmetric tensors.- Surfaces which behave like vortex lines.- On the spin geometry of supergravity and string theory.- Conic sub-Hilbert-Finsler structure on a Banach manifold.- On Spherically Symmetric Finsler metrics.-Part VI: Topics in Spectral Theory.- Homogeneous rank one perturbations and inverse square potentials.- Generalized Unitarity Relation for Linear Scattering Systems in One Dimension.- Differential equations on polytopes: Laplacians and Lagrangian manifolds, corresponding to semiclassical motion.-Part VII: Representation Theory.- Coadjoint orbits in representation theory of pro-Lie groups.- Conformal symmetry breaking on differential forms and some applications.- Representations of the anyon commutation relations.-Part VIII: Special Topics.- Remarks to the Resonance-Decay Problemin Quantum Mechanics from a Mathematical Point of View.- Dynamical generation of grapheme.- Eight kinds of orthogonal polynomials of Weyl group C2 and tau method.- Links between quantum chaos and counting problems.- Part IX: Extended Abstracts of the Lectures at “School on Geometry and Physics”.- Integral invariants (Poincaré-Cartan) and hydrodynamics.- Invitation to Hilbert C∗ -modules and Morita-Rieffel equivalence.- After Plancherel formula.- A glimpse of noncommutative geometry.- An Example of Banach and Hilbert manifold: the universal Teichmüller space.- Extensions of Symmetric Operators and Evolution Equations on Singular Spaces.