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Umfang: XVII, 670 p. 100 illus., 50 illus. in color. , online resource.

Ausgabe: 1st ed. 2021.

ISBN: 9783030557775

Serie: CRM Series in Mathematical Physics

Inhalt: This volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montréal, Canada from July 1-5, 2019. The main objective of the meeting was to share and make accessible new research and recent results in several branches of Theoretical and Mathematical Physics, including Algebraic Methods, Condensed Matter Physics, Cosmology and Gravitation, Integrability, Non-perturbative Quantum Field Theory, Particle Physics, Quantum Computing and Quantum Information Theory, and String/ADS-CFT. There was also a special session in honour of Decio Levi. The volume is divided into sections corresponding to the sessions held during the symposium, allowing the reader to appreciate both the homogeneity and the diversity of mathematical tools that have been applied in these subject areas. Several of the plenary speakers, who are internationally recognized experts in their fields, have contributed reviews of the main topics to complement the original contributions. .

Anmerkung: Chapter 1.Spin chains of Haldane-Shastry type: a bird's eye view. -Chapter 2.Features of discrete integrability -- Chapter 3.Darboux-Backlund transformations for Spin-valued linear problems -- Chapter 4.Painlev e IV transcendents generated from the complex oscillator -- Chapter 5.The Veronese sequence of analytic solutions of the CP2s sigma model equations described via Krawtchouk polynomials -- Chapter 6.A novel integrable fourth-order di erence equation admitting three invariants -- Chapter 7.Weighted Hurwitz numbers, -functions and matrix integrals -- Chapter 8.Constant curvature holomorphic solutions of the Constant curvature holomorphic solutions of the supersymmetric G(2; 4) sigma model -- Chapter 9.How to deal with nonlocality and pseudodi erential operators. An example: the Salpeter equation -- Chapter 10.A new approach to analysis of 2D higher order quantum superintegrable systems -- Chapter 11.Ladder operators and rational extensions -- Chapter 12.Tachyons and Representations of Sp(2;R) -- Chapter 13.A Confined Quasi-Maximally Superintegrable N-dimensional System, Classical and Quantum, in a Space with Variable Curvature -- Chapter 14.Conditional discretization of a generalized reaction-di usion equation -- Chapter 15.Discrete Curve Flows in Two-Dimensional Cayley{Klein Geometries -- Chapter 16.Zernike system stems from free motion on the 3-sphere -- Chapter 17.W-algebras via Lax type operators -- Chapter 18.Color Algebraic Extension of Supersymmetric Quantum Mechanics -- Chapter 19.The Racah algebra and sln -- Chapter 20.On Reducible Verma Modules over Jacobi Algebra -- Chapter 21.Howe duality and algebras of the Askey{Wilson type: an overview -- Chapter 22.Second-order supersymmetric partners of the trigonometric Rosen-Morse potential -- Chapter 23.A noncommutative geometric approach to the Batalin-Vilkovisky construction -- Chapter 24.A new method for constructing squeezed states for the isotropic 2D harmonic oscillator -- Chapter 25.Projective representations of the inhomogeneous symplectic group: Quantum symmetry origins of the Heisenberg commutation relations -- Chapter 26.Electron in bilayer graphene with magnetic elds associated to solvable potentials -- Chapter 27.Twist Knot Invariants and Volume Conjecture -- Chapter 28.Demazure Formulas for Weight Polytopes -- Chapter 29.Point transformations: exact solutions of the quantum timedependent mass nonstationary oscillator -- Chapter 30.Influence of the Electron-Phonon Interaction on the Topological Phase Transition in BiTeI -- Chapter 31.Nonlinear coherent states for anisotropic 2D Dirac materials -- Chapter 32.Monopole operators and their symmetries in QED3-Gross-Neveu models -- Chapter 33.Critical exponents for the valence-bond-solid transition in lattice quantum electrodynamics -- Chapter 34.Emergent geometry from entanglement structure -- Chapter 35.Interplay of Coulomb repulsion and spin-orbit coupling in superconducting 3D quadratic band touching Luttinger semimetals -- Chapter 36.Soft degrees of freedom, Gibbons-Hawking contribution and entropy from Casimir effect -- Chapter 37.Probes in AdS3 Quantum Gravity -- Chapter 38.Fundamental Physics, the Swampland of E ective Field Theory and Early Universe Cosmology -- Chapter 39.Scale-invariant scalar eld dark matter through the Higgs portal -- Chapter 40.The moduli portal to dark matter particles -- Chapter 41.Unified Superfluid Dark Sector -- Chapter 42.de Sitter Vacua in the String landscape: La Petite Version -- Chapter 43.Intensity mapping: a new window into the cosmos -- Chapter 44.Aberration in Gravito-Electromagnetism -- Chapter 45.Stable, thin wall, negative mass bubbles in de Sitter space-time -- Chapter 46.Ferromagnetic instability in PAAI in the sky -- Chapter 47.Three partial di erential equations in curved space and their respective solutions -- Chapter 48.What does the Central Limit Theorem have to say about General Relativity? -- Chapter 49.Dressing for a vector modi ed KdV hierarchy -- Chapter 50.Time evolution in quantum systems and stochastics -- Chapter 51.Solvable Models of Magnetic Skyrmions -- Chapter 52.Applications of Symmetry to the Large Scale Structure of the Universe (scale invariance) the to the hadronic spectrum -- Chapter 53.Leptophobic Z0 in supersymmetry and where to find them -- Chapter 54.Axion-like Particles, Magnetars, and X-ray Astronomy -- Chapter 55.Anomalies in B Decays: A Sign of New Physics? -- Chapter 56.Loopholes in WR searches at the LHC -- Chapter 57.t-t-h, top & bottom partners, and the Brane-Higgs limit -- Chapter 58.Mirror Dirac leptogenesis -- Chapter 59.Fast tests for probing the causal structure of quantum processes -- Chapter 60.Qubits as edge state detectors: illustration using the SSH model -- Chapter 61.RepLAB: a computational/numerical approach to representation theory.

In: Springer Nature eBook

Weitere Ausg.: Printed edition: ISBN 9783030557768

Weitere Ausg.: Printed edition: ISBN 9783030557782

Weitere Ausg.: Printed edition: ISBN 9783030557799

Sprache: Englisch

DOI: 10.1007/978-3-030-55777-5

URL: https://doi.org/10.1007/978-3-030-55777-5

URL: Volltext  (URL des Erstveröffentlichers)

URL: lizenzpflichtig

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Umfang: 1 online resource (646 pages)

ISBN: 3-030-55777-4

Serie: CRM Series in Mathematical Physics

Anmerkung: Intro -- Preface -- Organization -- Organizing Committee -- International Advisory Board -- QTS Conference Board -- Plenary Speakers -- Session Organizers -- Sponsors -- Statement of Principles -- Contents -- Part I Special Session in Honour of Decio Levi: Integrability: Continuous and Discrete, Classical & -- Quantum -- Spin Chains of Haldane-Shastry Type: A Bird's Eye View -- 1 Introduction -- 2 Calogero-Sutherland Models -- 2.1 The Calogero Model -- 2.2 The Sutherland Model -- 3 Spin Dynamical Models -- 3.1 The AN-1 Spin Calogero Model -- 4 Spin Chains of Haldane-Shastry Type -- 4.1 The Chain Sites -- 4.2 The Partition Function -- 5 Supersymmetric Spin Chains -- 5.1 The su(m|n) Supersymmetric Exchange Operator -- 5.2 Chemical Potential -- 5.3 Partition Function -- 6 Associated Vertex Models -- 7 Thermodynamics -- 7.1 Example: The su(1|1) Case -- 8 Conclusions -- References -- Features of Discrete Integrability -- 1 Introduction -- 2 What Is a Quad Equation? -- 3 A Few Standard Features of Integrable Quad Equations -- 3.1 Discrete Lax Pairs -- 3.2 Consistency Around the Cube (CAC) -- 3.3 Lax Pair from the Consistency Around the Cube -- 3.4 Symmetries -- 3.5 Singularity Analysis -- 3.6 Complexity Analysis: Algebraic Entropy -- 3.7 What About Quad Equations? -- 4 A Case Study -- 4.1 Symmetries -- 4.2 A Lax Pair -- 4.3 What About Singularities? -- 4.4 What About Entropy? -- 5 Comments and Perspectives -- References -- Darboux-BäcklundTransformationsforSpin-ValuedLinearProblems -- 1 Introduction -- 2 Clifford Algebras, Spin Groups, and Isometries of Rp,q -- 3 Spin-Valued Linear Problems -- 3.1 Geometric Interpretation: Soliton Surfaces Approach -- 4 Darboux-Bäcklund Transformations -- 4.1 The Darboux-Bäcklund Transformation in the Case of Spin Groups -- 5 Conclusions and Open Problems -- References. , Painlevé IV Transcendents Generated from the Complex Oscillator -- 1 Introduction -- 2 Supersymmetric Quantum Mechanics -- 3 Polynomial Heisenberg Algebras -- 3.1 Second-Degree PHA -- 4 Complex Oscillator -- 5 SUSY Partners of the Complex Oscillator -- 6 PIV Transcendents -- 7 Conclusions -- References -- The Veronese Sequence of Analytic Solutions of the CP2s Sigma Model Equations Described via Krawtchouk Polynomials -- 1 The CP2s Sigma Model -- 2 Projective Formalism -- 3 Solutions of the CP2s Sigma Model -- 4 The su(2) Spin-s Representation -- 5 Geometrical Aspects of Surfaces -- References -- A Novel Integrable Fourth-Order Difference Equation Admitting Three Invariants -- 1 Introduction -- 2 Integrability of Difference Equations -- 3 A Novel Example -- 4 Final Remarks -- References -- Weighted Hurwitz Numbers, τ-Functions, and Matrix Integrals -- 1 Hurwitz Numbers: Classical and Weighted -- 1.1 Geometric Meaning of Classical Hurwitz Numbers -- 1.2 Weighted Hurwitz Numbers GH1, HO1, H1, GH2 -- 2 Hypergeometric τ-Functions as Generating Functions for Weighted Hurwitz Numbers GH1, HO1, H1, GH2 -- 3 Wronskian and Matrix Integral Representation of τ(G,β)([X]) -- 3.1 Adapted Basis, Recursion Operators, Quantum Spectral Curve -- 3.2 Quantum and Classical Spectral Curve -- Rational Weighting Case -- Mellin-Barnes Integral Representation: Meijer G-Functions BH, HR -- Quantum Case Expressed as Mellin-Barnes Integrals HR -- 3.3 Determinantal Representation of τ(G,β)(t) -- Eulerian Wronskian Representation -- 3.4 Matrix Integral Representation of τ(G,β)([X]) BH, HR -- Wronskian Representation: Rational Case -- Matrix Integral Representation of τ(G,β)([X]): Rational Case -- Wronskian Representation: Quantum Case -- Matrix Integral Representation of τ(G,β)([X]): Quantum Case -- References. , Constant Curvature Holomorphic Solutions of the Supersymmetric G(2,4) Sigma Model -- 1 Introduction -- 2 CCH Solutions of the Susy G(M,N) σ-Model -- 2.1 Susy Invariant Solutions -- 3 CCH Solutions of the Susy G(2,4) σ-Model -- 3.1 The Case of Z1 -- 3.2 The Case of Z2 -- 3.3 The Case of Z3 -- 3.4 The Case of Z4 -- 4 Conclusions and Final Comments -- References -- How to Deal with Nonlocality and Pseudodifferential Operators. An Example: The Salpeter Equation -- 1 The Spinless Salpeter Equation: An Introduction -- 2 Solutions of the Salpeter Equation -- 3 A Recursive Solution: Nonlocality via Laplace Transform -- References -- A New Approach to Analysis of 2D Higher Order Quantum Superintegrable Systems -- 1 Introduction -- 2 The Canonical Form for a Symmetry Operator -- 3 Third Order Superintegrability -- 4 Some Examples (Mostly New) -- References -- Ladder Operators and Rational Extensions -- 1 Introduction -- 2 Maya Diagrams -- 3 Rational Extensions -- 4 Categorical Structure -- 5 Ladder Operators -- 6 Examples -- References -- Tachyons and Representations of Sp(2,R) -- 1 Introduction -- 2 SO0(2,3), Sp(2,R), the Poincaré Group and Their Lie Algebras -- 3 Algebraic Results -- 4 Representations -- References -- A Confined Quasi-Maximally Superintegrable N-dimensional System, Classical and Quantum, in a Space with Variable Curvature -- 1 The Classical Model: General Features -- 1.1 Metrics and Scalar Curvature -- 1.2 Solution of the Radial Equation of Motion -- 2 The Quantum Model -- 3 Concluding Remarks and Future Perspectives -- References -- Conditional Discretization of a Generalized Reaction-DiffusionEquation -- 1 Introduction -- 2 Case 1 -- 2.1 Symmetry Reduced Equations and Solutions -- 2.2 Construction of the Discretized Equation -- 3 Case 4 -- 3.1 Symmetry Reduced Equations and Solutions -- 3.2 Construction of the Discretized Equation. , 4 Conclusions -- References -- Discrete Curve Flows in Two-Dimensional Cayley-Klein Geometries -- 1 Introduction -- 2 Cayley-Klein Planes -- 3 Moving Frames -- 4 Recurrence Relations -- 4.1 Exterior Derivative -- 4.2 Shift Map -- 5 Invariant Linearization Operators -- 6 Geometric Flows -- References -- Zernike System Stems from Free Motion on the 3-Sphere -- 1 Introduction: The so(4) Algebra -- 2 Realization of SO(4) on the 3-Sphere -- 3 Two Coordinate Systems for S3 -- 4 Projection on the 2-Sphere S2 -- 5 Interbasis Expansion Coefficients -- 6 Concluding Remarks -- References -- Part II Algebraic and Non-perturbative Methods -- W-Algebras via Lax Type Operators -- 1 Introduction -- 2 What Is a W-Algebra? -- 2.1 Fundamental Physical Theories and Corresponding Fundamental Algebraic Structures -- (Poisson) Vertex Algebras -- Vertex Algebras -- 2.2 A Toy Model -- 2.3 Hamiltonian Reduction -- 2.4 From the Toy Model to W-Algebras -- Classical Finite W-Algebras -- Finite W-Algebras -- Classical Affine W-Algebras -- Quantum Affine W-Algebras -- 3 Linear Algebra Intermezzo -- 3.1 Set Up -- 3.2 The ``Identity'' Notation -- 3.3 Generalized Quasideterminants -- 4 Quantum Finite W-Algebras and (Twisted) Yangians -- 4.1 Lax Type Operators for Quantum Finite W-Algebras -- 4.2 The Generalized Yangian Identity -- 4.3 Quantum Finite W-Algebras and (Extended) Twisted Yangians -- 5 Classical Affine W-Algebras and Integrable Hierarchies of Lax Type Equations -- 5.1 Lax Type Operators for Classical Affine W-Algebras -- 5.2 Integrable Hierarchies of Lax Type Equation -- References -- Color Algebraic Extension of Supersymmetric Quantum Mechanics -- 1 Introduction -- 2 Z2n-Graded Color Superalgebra and Z22-Graded SQM -- 3 Extensions of Bruce-Duplij Model -- 3.1 From Superalgebra to Z22-Graded Color Superalgebra -- 3.2 N Extension of Z22-Graded SQM -- 3.3 Z22-Graded SCM. , 4 Z23-Graded SQM -- References -- The Racah Algebra and sln -- 1 Introduction -- 2 Definition of the Higher Rank Racah Algebra -- 3 Realizing sln in n-1 Variables -- 3.1 Some Operators in U(Dn) -- 4 Realization of Rn in n-2 Variables -- 4.1 The Differential Embedding -- 5 Conclusions -- References -- On Reducible Verma Modules over Jacobi Algebra -- 1 Introduction -- 2 Preliminaries -- 3 Case G2 -- 4 Verma Modules and Singular Vectors -- 4.1 Definitions -- 4.2 Case G2 -- Weight 2δ1 -- Weight 2δ2 -- Weight δ1+δ2 -- Weight δ1-δ2 -- Weight δ1 -- Weight δ2 -- Weight 3δ2 -- References -- Howe Duality and Algebras of the Askey-Wilson Type: An Overview -- 1 Introduction -- 2 General Framework -- 3 The Dual Presentations of the Racah Algebra -- 4 More Dual Pictures: An Overview -- 4.1 The Racah Family -- 4.2 The Bannai-Ito Ensemble -- 4.3 The Askey-Wilson Class -- 5 Conclusion -- References -- Second-Order Supersymmetric Partners of the Trigonometric Rosen-Morse Potential -- 1 Introduction -- 2 Supersymmetric Quantum Mechanics -- 3 Trigonometric Rosen-Morse Potential -- 4 SUSY Partners of the Trigonometric Rosen-Morse Potential -- 5 Conclusions -- References -- A Noncommutative Geometric Approach to the Batalin-Vilkovisky Construction -- 1 Introduction: Why Noncommative Geometry -- 2 Finite Spectral Triples and Induced Gauge Theories -- 3 The BV Construction in the Algebraic Context -- 4 BV-Spectral Triple: The Notion and the Relevance -- 5 Conclusions and Outlooks -- References -- A New Method for Constructing Squeezed States for the Isotropic 2D Harmonic Oscillator -- 1 Introduction -- 2 Squeezed States of the 1D Harmonic Oscillator -- 3 The 2D Oscillator -- 4 SU(2) Coherent States -- 5 2D Squeezed States -- 6 Conclusion -- References -- Electron in Bilayer Graphene with Magnetic Fields Associated with Solvable Potentials -- 1 Introduction. , 2 Bilayer Graphene: A Brief Overview.

Weitere Ausg.: ISBN 3-030-55776-6

Sprache: Englisch