Lie Theory and Its Applications in Physics Sofia Bulgaria June 2021 1st Edition by Vladimir Dobrev 9811947503 9789811947506

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ISBN 10: 9811947503

ISBN 13: 9789811947506

Author: Vladimir Dobrev

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 (on-line) in June 2021. 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 big interdisciplinary and interrelated field. The topics covered in this Volume are the most modern trends in the field of the Workshop: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, Exceptional quantum algebra for the standard model of particle physics, Gauge Theories and Applications, Structures on Lie Groups and Lie Algebras. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Lie Theory and Its Applications in Physics Sofia Bulgaria June 2021 1st Table of contents:

Part I. Plenary Talks

Multiplicity in Restricting Minimal Representations

From the String Landscape to the Mathematical Landscape: A Machine-Learning Outlook

Octonionic Clifford Algebra for the Internal Space of the Standard Model

The Jacobi Sigma Model

Levi-Civita Connections on Braided Algebras

Notes on AdS Holography and Higher-Derivative Supergravity

Homothetic Rota–Baxter Systems and Dyck-Algebras

Quantum Dynamics Far from Equilibrium: A Case Study in the Spherical Model

On First Extensions in -Subcategories of

Higher Dimensional CFTs as 2D Conformally-Equivariant Topological Field Theories

Reducing the N = 1, 10-d, Gauge Theory over a Modified Flag Manifold

Part II. String Theories, (Super-)Gravity, Cosmology

Ramond States of the D1-D5 CFT Away from the Free Orbifold Point

Primordial Black Hole Generation in a Two-Field Inflationary Model

Late Time Cosmic Acceleration with Uncorrelated Baryon Acoustic Oscillations

On the Hidden Symmetries of Supergravity

Defects at the Intersection: The Supergroup Side

A New S-matrix Formula and Extension of the State Space in Open String Field Theory

Dual Dilaton with and Fluxes

Part III. Representation Theory

On 1-Dimensional Modules over the Super-Yangian of the Superalgebra Q(1)

A Klein Operator for Paraparticles

Principal and Complementary Series Representations at the Late-Time Boundary of de Sitter

Bulk Reconstruction from a Scalar CFT at the Boundary by the Smearing with the Flow Equation

Building Momentum Kernel from Shapovalov Form

Action of on for Orthogonal and Exceptional Groups

Pairs of Spectral Projections of Spin Operators

Part IV. Integrable Systems

Algebraic Engineering and Integrable Hierarchies

Nested Bethe Ansatz for RTT–Algebra

Lie Reductions and Exact Solutions of Generalized Kawahara Equations

Several Exactly Solvable Quantum Mechanical Systems and the SWKB Quantization Condition

Automorphic Symmetries and Integrable Deformations

Part V. Applications to Quantum Theory

The Conformal-Symmetry–Color-Neutrality Connection in Strong Interaction

Gaudin Model with General Boundary Terms

Entanglement of Mixed States in Kähler Quantization

The Chirality-Flow Formalism for Standard Model Calculations

Spacetime Stochasticity and Second Order Geometry

Part VI. Special Mathematical Results

Velocity Reciprocity in Flat and Curved Space-Time

Meta-Schrödinger Transformations

The Quantum Mirror to the Quartic del Pezzo Surface

Bidirectional Processes—In Category Theory, Physics, Engineering, …

Part VII. Gauge Theories and Applications

Nonholomorphic Superpotentials in Heterotic Landau-Ginzburg Models

Automorphic Forms and Fermion Masses

Wilson Lines and Their Laurent Positivity

Gauging Higher-Spin-Like Symmetries Using the Moyal Product

Integration of Double Field Theory Algebroids and Pre-rackoid in Doubled Geometry

Doubled Aspects of Algebroids and Gauge Symmetry in Double Field Theory

Lie Algebroids and Weight Systems

Part VIII. Structures on Lie Groups and Lie Algebras

Visible Actions of Certain Affine Transformation Groups of a Siegel Domain of the Second Kind

Quantum Particle on Lattices in Weyl Alcoves

Abelian J-Invariant Ideals on Nilpotent Lie Algebras

The Dihedral Dunkl–Dirac Symmetry Algebra with Negative Clifford Signature

Lie Structure on Hopf Algebra Cohomology

Filtration Associated to an Abelian Inner Ideal and the Speciality of the Subquotient of a Lie Algebra

Nilpotent Inner Derivations in Prime Superalgebras

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