Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1: QTS-X/LT-XII, Varna, Bulgaria, June 2017 (Springer Proceedings in Mathematics & Statistics (263))

This book is the first volume of proceedings from the joint conference X International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), held on 19-25 June 2017 in Varna, Bulgaria. The QTS series was founded on the core principle that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium at the forefront of theoretical and mathematical physics. The LT series covers the whole field of Lie theory in its widest sense, together with its applications in many areas of physics. As an interface between mathematics and physics, the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In dividing the material between the two volumes, the Editor has sought to select papers that are more oriented toward mathematics for the first volume, and those focusing more on physics for the second. However, this division is relative, since many papers are equally suitable for either volume. The topics addressed in this volume represent the latest trends in the fields covered by the joint conferences: representation theory, integrability, entanglement, quantum groups, number theory, conformal geometry, quantum affine superalgebras, noncommutative geometry. Further, they present various mathematical results: on minuscule modules, symmetry breaking operators, Kashiwara crystals, meta-conformal invariance, the superintegrable Zernike system. [source : 4e de couverture] Front Matter ....Pages i-xv Front Matter ....Pages 1-1 Image of Conformally Covariant, Symmetry Breaking Operators for \({\mathbb {R}}^{p,q}\) (Toshiyuki Kobayashi, Alex Leontiev)....Pages 3-35 Trails for Minuscule Modules and Dual Kashiwara Functions for the \(B(\infty )\) Crystal (Anthony Joseph)....Pages 37-53 From Euler’s Play with Infinite Series to the Anomalous Magnetic Moment (Ivan Todorov)....Pages 55-73 On the Derivation of the Wallis Formula for \(\pi \) in the 17th and 21st Centuries (Tamar Friedmann)....Pages 75-89 Variations of Infinite Derivative Modified Gravity (Ivan Dimitrijevic, Branko Dragovich, Zoran Rakic, Jelena Stankovic)....Pages 91-111 Infinite-Dimensional Metaconformal Symmetries: 1D Diffusion-Limited Erosion and Ballistic Transport in \((1+2)\) Dimensions (Malte Henkel, Stoimen Stoimenov)....Pages 113-135 Behrends–Fronsdal Spin Projection Operator in Space-Time with Arbitrary Dimension (A. P. Isaev, M. A. Podoinitsyn)....Pages 137-148 Wakimoto Realization of the Quantum Affine Superalgebra \(U_q(\widehat{sl}(M|N))\) (Takeo Kojima)....Pages 149-163 On Superdimensions of Some Infinite-Dimensional Irreducible Representations of \(\mathfrak {osp}(m|n)\) (N. I. Stoilova, J. Thierry-Mieg, J. Van der Jeugt)....Pages 165-176 Non-commutativity in Unified Theories and Gravity (G. Manolakos, G. Zoupanos)....Pages 177-205 Front Matter ....Pages 207-207 Webs of Quantum Algebra Representations in 5d \({\mathcal {N}}=1\) Super Yang–Mills (Jean-Emile Bourgine)....Pages 209-218 Parallelizations for Induced Representations of \(\text {SO}_0(2,q)\) (Patrick Moylan)....Pages 219-229 Jordan Algebra and Hydrogen Atom (Todor Popov)....Pages 231-244 Screening Operators for the Lattice Vertex Operator Algebras of Type \(A_1\) at Positive Rational Level (Takuya Matsumoto)....Pages 245-253 Symmetries of the \(S_3\) Dirac–Dunkl Operator (Hendrik De Bie, Roy Oste, Joris Van der Jeugt)....Pages 255-260 Front Matter ....Pages 261-261 The Superintegrable Zernike System (Natig M. Atakishiyev, George S. Pogosyan, Cristina Salto-Alegre, Kurt Bernardo Wolf, Alexander Yakhno)....Pages 263-273 The Two Bosonizations of the CKP Hierarchy: Bicharacter Construction and Vacuum Expectation Values (Iana I. Anguelova)....Pages 275-292 Recursion Operator and Bäcklund Transformation for Super mKdV Hierarchy (A. R. Aguirre, J. F. Gomes, A. L. Retore, N. I. Spano, A. H. Zimerman)....Pages 293-309 Lie Symmetry Analysis of a Third-Order Equation Arising from a General Class of Lotka–Volterra Chains (Kyriakos Charalambous, Christodoulos Sophocleous)....Pages 311-318 Front Matter ....Pages 319-319 Probing Anderson Localization Using the Dynamics of a Qubit (Hichem Eleuch, Michael Hilke, Richard MacKenzie)....Pages 321-329 Pure Spinors, Impure Spinors and Quantum Mechanics (Mike Hewitt)....Pages 331-335 Higher-Derivative Oscillators in \(AdS_5\times S^5\) T-Dual Penrose Limits (H. Dimov, S. Mladenov, R. Rashkov, T. Vetsov)....Pages 337-344 Front Matter ....Pages 345-345 A Unified Approach to Poisson–Hopf Deformations of Lie–Hamilton Systems Based on \(\mathfrak {sl}\)(2) (Ángel Ballesteros, Rutwig Campoamor-Stursberg, Eduardo Fernández-Saiz, Francisco J. Herranz, Javier de Lucas)....Pages 347-366 Two-Parameter Quantum General Linear Supergroups (Huafeng Zhang)....Pages 367-376 Noncommutative Geometry and An Index Theory of Infinite-Dimensional Manifolds (Doman Takata)....Pages 377-381 Front Matter ....Pages 383-383 A Stable Version of Terao Conjecture (Cristian Anghel)....Pages 385-391 Multiplication of Distributions and Nonperturbative Calculations of Transition Probabilities (J. F. Colombeau, J. Aragona, P. Catuogno, S. O. Juriaans, C. Olivera)....Pages 393-401 About Markov, Gibbs, ... Gauge Theory ... Finance (Alexander Ganchev)....Pages 403-412 A Method for Classifying Filiform Lie Superalgebras (Rosa M. Navarro, José M. Sánchez)....Pages 413-420 Equivalence of Vector Field Realizations of Lie Algebras from the Lie Group Point of View (Maryna Nesterenko, Severin Pošta)....Pages 421-427