This volume collects papers based on lectures given at the XXXIX Workshop on Geometric Methods in Physics, held in Biaystok, 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.

  Provides an overview of cutting-edge research in geometry, analysis, and a wide variety of other areas Offers insight into recent developments at the intersection of mathematics and physics Collects papers based on lectures given at the XXXIX Workshop on Geometric Methods in Physics in June 2022

  Autorentext

  Dr. Piotr Kielanowski is a professor of theoretical and mathematical physics at the Center for Research and Advanced Studies of the Polytechnic University of Mexico in Mexico City. He has published more than 80 original papers in the field of particle phenomenology and has mentored several PhD students. He is the co-author of a book on quantum mechanics (Quantum Physics: States, Observables and Their Time Evolution, Springer, 2019). He has been a member of the Organizing Committee of the Biäowie a Workshop on Geometric Methods in Physics for about 20 years, and has been the editor of successive volumes of the proceedings.

Dr. Alina Dobrogowska is a professor in the Faculty of Mathematics of the University of Biäystok, Poland. She has published numerous papers on integrable systems, particularly in relation to factorization methods, bihamiltonian systems, q-difference equations and Lie algebroids. She has been a member of the Organizing Committee of the Workshopsince 2001, and since last year she is the chairman of the Organizing Committee.

Dr. Gerald A. Goldin is a distinguished professor of mathematics, physics, and mathematics education at Rutgers University in New Brunswick, New Jersey. His work in mathematical physics focuses on local current algebras and their representations, measures on infinite-dimensional configuration spaces, quantum vortex configurations, nonlinear electrodynamics, and nonlinear variations of quantum mechanics. With colleagues at Los Alamos National Laboratory, he was an early co-discoverer of the possibility of "anyon" and "nonabelian anyon" statistics. He is a recipient of the Alexander von Humboldt Research Prize in physics, and has been a Workshop participant for over 30 years.

Dr. Tomasz Goli ski is an assistant professor in the Faculty of Mathematics of the University of Biäystok, Poland. His research interests address various aspects of mathematical physics, with emphasis on topics related to problems of functional analysis and operator algebras. These include infinite dimensional geometry with emphasis on Poisson geometry on Banach manifolds, Banach Lie groupoids and algebroids, integrable systems, and factorization methods in their discrete version. He has been Secretary of the Workshop since 2003.

Inhalt

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 PoissonLie 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 Szego 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).