This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held in Sofia (Bulgaria) in June 2023.
Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field.
The topics covered in this volume from the workshop represent the most modern trends in the field: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics
This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
Plenary Talks, T. Kobayashi, Short Proof for RankinCohen Brackets and
Generating Operators.- I. Todorov, The 2022 Nobel Prize in Physics.- P.
Aschieri, G. Landi, C. Pagani, Quantum Gauge Groups of Quantum Principal
Bundles.- D. Broadhurst, Multivariate Elliptic Kites and Tetrahedral
Tadpoles.- S. Catto, Hurwitz Algebras at the Core of Classication of
Possible Symmetries in Hadronic Physics.- E. Guendelman, Braneworlds in
Dynamical Tension String Theories.- M. Henkel, Generalised
Time-Translation-Invariance in Simple Ageing.- V. Avramov, R. C. Rashkov, T.
Vetsov, Remarks on Operator Growth and Certain Integrable Structures.-
Nedialka I. Stoilova and Joris Van der Jeugt, Matrix Structure of Classical
Z2 × Z2 Graded Lie Algebras.- G. Patellis, W. Porod and G. Zoupanos, Split
NMSSM from Dimensional Reduction of a 10D, N = 1, E8 Theory Over a Modied
Flag Manifold.- String Theories, Gravity, Cosmology, L. Anguelova and C.
Lazaroiu, Consistency Condition for Slow-roll and Rapid-turn Ination.- I.
Dimitrijevic“, B. Dragovich, Z. Rakic and J. Stankovic, On a Nonlocal de
Sitter Gravity.- Denitsa Staicova, Cosmology in LIV Constraints from GRB
Time-Delays.- H. Kunitomo, Superstring Field Theory with Homotopy Lie Algebra
Structure.- V. Avramov, M. Radomirov, R.C. Rashkov and T. Vetsov, Classical
Thermodynamic Stability of Reissner-Nordstrom-AdS Black Hole.-
Supersymmetry, E. Poletaeva, On Dual Modules over the Super-Yangian of Q(1).-
N. Aizawa, Towards a Supereld Formulation of Z22-Supersymmetry.- A. Nedelin,
Elliptic Integrable Models and Their Spectra from Superconformal Indices.- N.
Hage, A Super LittlewoodRichardson Type Rule.- Integrable Systems.- C.
Burdk and O. Navratil, Dependence of Bethe Vectors for RTTType Algebra
sp(4).- O. Vaneeva, O. Brahinets, O. Magda, A. Zhalij, Equivalence Groupoid
and Exact Solutions of a Class of Generalized Modied Kortewegde Vries
Equations.- N. Manojlovic and I. Salom, Bethe states for the periodic
inhomogeneous SO(3) spin chain.- R. Abedin and S. Maximov, Twisted Standard
Lie Bialgebra Structures on Loop Algebras.- Y. Nasuda, Harmonic Oscillator
with a Step and Its Wigner Function.- T. Prochazka, W -Algebras and
Integrability.- Representation Theory, K. Arashi, Coherent State
Representations of the Holomorphic Automorphism Group of a Quasi-Symmetric
Siegel Domain of Type III.- P. Spacek and C. Wang, Canonical Mirror Models
for Maximal Orthogonal Grassmannians.- B. Westbury, Series of
Representations.- R. Stekolshchik, Remarks on Decompositions of the Longest
Element of the Weyl Group.- V. Losert, On Matrix Coefcients of
Representations of SL(2, R).- V. K. Dobrev, Quaternionic Discrete Series and
Invariant Differential Operators over the Lie Algebra F40.- Various
Mathematical Results, A. Dobrogowska, Lie Algebroid Structures on Cotangent
Bundles Determined by Vector Fields.- Valdemar V. Tsanov, Partial Convex
Hulls of Coadjoint Orbits and Degrees of Invariants.- R. Campoamor-Stursberg
and M. Rausch de Traubenberg, Kac-Moody and Virasoro Algebras on the
Two-Sphere and the Two-Torus.- F. Januszewski, Families of D-Modules and
Integral Models of (g, K)-Modules.- A. Mayeux, Magnets and Attractors of
Diagonalizable Group Schemes Actions.- V. C. Bui, V. Hoang Ngoc Minh, Q.H.
Ngo and V. Nguyen Dinh, On the Kernels of the Polymorphism Zeta.- C. Anghel
and D. Cheptea, Ribbon Structures Derived from Homotopy Leibniz Algebras and
Symplectic Lie Pairs.- Conformal Theories, T. Kojima, Quadratic Relations of
the Deformed W -Algebra.- S. Stoimenov and M. Henkel, Meta-Schrodinger and
Meta-Conformal Symmetries in the Non-Equilibrium Dynamics of the Directed
Spherical Model.- D. Klyuev, A Different Approach to Positive Traces
on Generalized q-Weyl Algebras.- Gizem Søeng, Searching for Discrete Series
Representations at the Late-Time Boundary of de Sitter, H. Pejhan, de Sitter
Relativity Group.- Applications of Holography, Ph. Nounahon and Todor Popov,
Landau Levels for the Haldanes Spheres.- V. Avramov, H. Dimov, M. Radomirov,
R.C. Rashkov, T. Vetsov, Thermodynamic Length and Optimal Processes in
Holographic Models.- Chen-Te Ma, Modular Average and Weyl Anomaly in
Two-Dimensional Schwarzian Theory.- Applications to Quantum Theory, A. Sako,
Lie Algebra and Quantization in Quantum World.- Otto C.W. Kong, Lorentz
Covariant Quantum Particle Dynamics from the Proper Symmetry Theoretical
Formulation.- E. I. Jafarov, S. M. Nagiyev, J. Van der Jeugt, The Semiconned
Harmonic Oscillator with a Position-Dependent Effective Mass: Exact Solution,
Dynamical Symmetry Algebra and Quasiprobability Distribution Functions.
