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Full Description
This volume collects papers based on lectures given at the XXXIX Workshop on Geometric Methods in Physics, held in Białystok, Poland in June 2022. These chapters provide readers an overview of cutting-edge research in geometry, analysis, and a wide variety of other areas. Specific topics include:
Classical and quantum field theories
Infinite-dimensional groups
Integrable systems
Lie groupoids and Lie algebroids
Representation theory
Geometric Methods in Physics XXXIX will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.
Contents
In Memoriam: Anatol Odzijewicz.- In Memoriam: Emma Previato.- Part I: Session in memory of Bogdan Mielnik: Incomplete visions. . (Mielnik).- Memories about Bogdan Mielnik (Krasi'nski).- Scattering states of the inverted oscillator and its supersymmetric partners (Bermudez).- The Klein paradox in the phase space quantum mechanics (Campobasso).- An Asymmetric Harmonic Oscillator (Chadzitaskos).- On the construction of position-dependent mass models with quadratic spectra (Cruz y Cruz).- Bogdan Mielnik's contributions to the factorization method (Fern'andez).- The 1 - D Dirac equation in the phase space quantum mechanics (Tosiek).- Canonical photon position operator with commuting components (Turrubiates).- Quantum version of the Euler's problem: a geometric perspective (Zyczkowski).- Part II: Contributions to the XXXIX Workshop: Solvable Lie groups with factor regular representations (Beltita).- Pedal coordinates and orbits inside magnetic dipole field (Blaschke).- Hidden Symmetries of the Type D Metrics (Breton).- On some structures of Lie algebroids on the cotangent bundles (Dobrogowska).- Predicting "Anyons": Implications of History for Science (Goldin).- Quadratic algebra and spectrum of superintegrable system (Hoque).- Unifying Classical & Quantum Physics + Quantum Fields & Gravity (Klauder).- Algebraic Quantum Field Theory and Causal Symmetric Spaces (Olafsson).- The parametrically extended Kardar-Parisi-Zhang equation, its dark type generalization and integrability (Prykarpatski).- Banach Poisson-Lie group structure on U(H) (Tumpach).- Symplectic realizations of e(3) (Wawreniuk).- On some developments of the Stokes phenomenon (Xu).- Comparison of two topologies on weighted Szeg˝o space (Zynda).- Part III: Abstracts of the Lectures at "XI School on Geometry and Physics: Lecture notes on quantization and group C∗-algebras (Beltit).- Supersymmetric quantum mechanics and Painlev'e IV transcendents (Fernandez).- On some concepts in the theory of Lie algebroids (Rotkiewicz).
