Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2: QTS-X/LT-XII, Varna, Bulgaria, June 2017 (Springer Proceedings in Mathematics & Statistics, 255)

This book is the second volume of the proceedings of 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), 19-25 June 2017, Varna, Bulgaria. The QTS series started around the core concept that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium on the frontiers 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 facets of physics. As an interface between mathematics and physics the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In the division of the material between the two volumes, the Editor has tried to select for the first and second volumes papers that are more oriented toward mathematics and physics, respectively. However, this division is relative since many papers could have been placed in either volume. The topics covered in this volume represent the most modern trends in the fields of the joint conferences: symmetries in string theories, conformal field theory, holography, gravity theories and cosmology, gauge theories, foundations of quantum theory, nonrelativistic and classical theories. [source : 4e de couverture] Preface of Volume 2......Page 6 Acknowledgements......Page 7 Contents......Page 8 List of Participants......Page 11 Summary......Page 15 Plenary Talks......Page 16 1 Introduction......Page 17 2 Integrable Spin Chain and Hexagon Form Factors......Page 18 3 Hexagonalisation and Fishnet Integrals......Page 23 4 Conclusion......Page 28 References......Page 29 1 Introduction......Page 31 2 A Few Examples in 3d and 4d......Page 33 3 Two-Point Correlators and Effective Actions......Page 35 4 The Local and Non-local Fronsdal Equations......Page 37 5.2 Tadpoles and Seagulls......Page 40 6 Comments......Page 42 References......Page 43 Algebraic Structures in Exceptional Geometry......Page 45 References......Page 52 Duality in the Sachdev-Ye-Kitaev Model......Page 56 1 Introduction......Page 57 2 Overview of SYK......Page 58 3 Bulk Space-Time......Page 61 4 3D Realization and c=1......Page 68 References......Page 73 1 Motivations and Contents......Page 75 2.1 Basic Superspaces......Page 77 2.2 Basic Superfields......Page 78 2.3 mathscrN=(1,0) Superfield Actions......Page 79 3 Higher-Dimension mathscrN=(1,0) and mathscrN=(1,1) Invariants......Page 80 4 mathscrN=(1,1) Harmonic Superspace......Page 81 5 Invariants in mathscrN=(1,1) Superspace......Page 83 6 Quantum mathscrN=(1,0) and mathscrN=(1,1) SYM......Page 84 7 Summary and Outlook......Page 85 References......Page 86 1 Introduction......Page 88 2.1 Physical and Mirror Channels......Page 90 2.2 Thermal Partition Function......Page 91 2.3 The Partition Function as a Sum over Mode Numbers......Page 92 2.4 From Mode Numbers to Rapidities......Page 94 2.5 Graph Expansion of the Gaudin Determinant......Page 95 2.6 Performing the Sum over Trees......Page 98 3 The Energy of an Excited State......Page 99 4 One-Point Functions at Finite Volume/Temperature......Page 101 4.1 The One-Point Function in Terms of Connected Diagonal Form Factors......Page 102 4.2 LeClair-Mussardo Series from the Tree Expansion......Page 103 4.3 The Case of a Conserved Charge......Page 105 5 Conclusion......Page 107 References......Page 108 Wheeler–DeWitt Quantization of Gravity Models of Unified Dark Energy and Dark Matter......Page 110 1 Introduction......Page 111 2.1 Hidden Noether Symmetry and Unification of Dark Energy and Dark Matter......Page 112 2.2 Quintessential Inflation and Unified Dark Energy and Dark Matter......Page 113 3 Wheeler–De Witt Minisuperspace Quantization......Page 118 4 Conclusions......Page 122 References......Page 123 1 Introduction......Page 125 2.1 Generalised Form Factors of Wilson Loops......Page 128 2.2 Dual Variables......Page 129 2.3 Duality Relation......Page 130 2.4 Duality Relation at MHV Level......Page 131 2.5 Duality Beyond MHV......Page 134 3.1 calN=4 Super-Yang-Mills in LHC Superspace......Page 137 3.2 Chiral Wilson Loop in LHC Superspace......Page 138 4 Diagrammatic Approach to the Duality......Page 139 4.1 MHV Example......Page 140 5 Concluding Remarks......Page 141 References......Page 144 1 Introduction......Page 146 1.1 Thermalization......Page 147 1.3 Localized Systems......Page 148 2 Many-Body Interacting Model by Using Coproducts......Page 149 2.1 Coproducts......Page 150 3 Eigenstates and Eigenvalues......Page 151 3.1 Level 1 States......Page 152 3.2 Level p States......Page 153 4 Entanglement Entropy......Page 155 5 Discussion......Page 156 References......Page 157 1 Introduction......Page 158 2 Cooperative Game Theory: The Whole is Greater than the Sum of Its Parts......Page 159 3 Generalized Bases of Mixed States with a Resolution of the Identity......Page 161 5.1 Location Indices, Comonotonic Operators and Comonotonicity Intervals......Page 164 6 Discussion......Page 166 References......Page 167 Holography and String Theory......Page 168 1 Introduction......Page 169 2 Constant Roll Inflation......Page 170 3 Parameter Space of the New Solutions......Page 172 4 Stability Under Scalar Perturbations......Page 173 5 Scalar Spectral Index......Page 175 6 Other Non-slow Roll Regimes......Page 177 References......Page 178 1 Introduction......Page 180 2 The Dp/Dq Brane Holographic Set-Up......Page 182 3 Holographic Calculation of the Condensate Susceptibility......Page 183 4 Field Theory Comparison......Page 184 5 Conclusion......Page 185 References......Page 186 1 Introduction and Summary......Page 187 2 Non-perturbative Scalars in the Wilson Loop......Page 188 3 Fermion Contribution to the Wilson Loop......Page 190 3.1 Emergence of a Bound State......Page 191 3.2 Mesons Bound States, TBA and Beyond......Page 194 References......Page 196 1 Introduction......Page 198 2 Four-Point String Amplitudes......Page 200 3.1 Linear Relations in Hard Limit......Page 203 3.2 Recurrence Relations in Regge Limit......Page 205 4 Symmetry of Four-Point Amplitudes at General Energy......Page 206 References......Page 208 1 Introduction......Page 210 2 Basics of Thermo Field Dynamics......Page 211 3 The Fisher Information Metric for Closed Strings in Plane Wave Geometry......Page 213 4 Reconstruction of Probability Density Functions from Fisher Metric......Page 216 References......Page 218 Gravity and Cosmology......Page 220 1 Introduction......Page 221 2.2 Duality Structures......Page 223 2.3 Electromagnetic Structures......Page 224 2.4 Scalar-Duality and Scalar-Electromagnetic Structures......Page 225 2.5 Pulled-Back Electromagnetic Structures......Page 226 2.6 The Mathematical Formulation of Generalized ESM Theories......Page 227 2.7 Sheaves of Scalar-Electromagnetic Configurations and Solutions......Page 228 3 Scalar-Electromagnetic Dualities and Symmetries......Page 229 4.1 Integral Duality Structures and Integral Electromagnetic Structures......Page 231 4.2 The Twisted Dirac Quantization Condition......Page 233 References......Page 234 1 Introduction......Page 236 2.1 Einstein–Scalar Theories with 2-Dimensional Scalar Manifolds......Page 237 2.2 Cosmological Models Defined by (Σ,mathcalG, V)......Page 238 3.1 Lifted Trajectories and Tilings......Page 239 3.3 Well-Behaved Scalar Potentials......Page 240 4 Examples of Trajectories for the Hyperbolic Triply Punctured Sphere......Page 241 References......Page 244 1 Introduction......Page 245 2 The BRST Formulation of Supergravity......Page 246 3 The Full Topological Structure of Supergravity......Page 247 4 The Cohomological Equations of Localization......Page 249 References......Page 252 1 The Two-Measures Model......Page 253 2 The Darkon Model in FLRW Metric......Page 254 3 The Two-Measures Theory – Including the Inflaton......Page 257 4 Conclusions......Page 261 References......Page 262 1 Introduction......Page 263 2 Basic Equations and Boundary Conditions......Page 264 3 Numerical Results......Page 265 References......Page 268 Conformal and Gauge Theories......Page 270 1 Introduction......Page 271 2 From Conformal Ward–Takahashi Identities to Intertwining Relations......Page 272 3 Timelike Conformal Killing Vectors Associated with the Subgroup SO(1,1)subsetSO(2,d)......Page 274 4 Intertwining Relations in the SO(1,1) Basis......Page 279 References......Page 281 1 Introduction......Page 283 2.1 The Theory......Page 284 2.2 Mixing of the Fields......Page 289 3 N=2 Superconformal Models......Page 292 References......Page 295 1 Introduction......Page 296 2.1 Solution: General Expressions......Page 298 3 Extremely Localized Input: Fundamental Solution......Page 299 3.1 Numerical Analysis: V-Like Shape of |S(ξ,τ)|2......Page 300 4 Gaussian Input......Page 301 5 Salpeter Equation and Optics......Page 302 5.1 Bessel Input: Band-Limited Initial Condition......Page 303 5.2 Coordinate-Momentum Representation: Wigner Distribution Function......Page 304 References......Page 306 1 Introduction......Page 307 2 The Standard Model Algebra......Page 308 3 Representing Leptons and Quarks......Page 310 4 The Gauge Symmetries......Page 312 5 Open Problems......Page 313 References......Page 314 Foundations of Quantum Theory......Page 315 1 Introduction......Page 316 2 Sketch of the Classical Background......Page 317 3 Setting of the Quantum Theory......Page 320 4 Lie Algebra of Special Phase Functions......Page 322 5 Quantum Symmetries......Page 325 References......Page 332 1 Introduction and Preliminaries......Page 334 2 The Frame Optimization Problem......Page 338 3.1 The Solution to the Quantum State Separability Problem......Page 339 3.2 Examples of (IC-POVMs)......Page 341 3.3 The Solution to the Quantum State Estimation Problem......Page 342 4.1 The Solution to the Quantum State Separability Problem......Page 343 4.2 Constructing Solutions to the Quantum State Separability Problem......Page 345 4.3 The Solution to the State Estimation Problem......Page 346 References......Page 347 1 Introduction......Page 350 2 General Structure of Lie Groups: Levi Decomposition......Page 352 3 A Classification of Poincaré Group Extensions......Page 353 4 Conservative Extensions of the Poincaré Group......Page 354 5 Commutation Relations of the Concrete Example......Page 356 References......Page 359 1 Introduction......Page 360 2 The Complement to Noether's Theorem......Page 361 3 Two-Particle States and Interaction......Page 363 4 Illustration: A Scattering Experiment......Page 365 5 Conclusions......Page 367 References......Page 368 1 Introduction......Page 369 2 Associated Laguerre Polynomials......Page 370 3 SU(2) Representations in the Plane......Page 372 4 Rigged Hilbert Space Formulation......Page 375 5 Conclusions......Page 377 References......Page 378 Nonrelativistic and Classical Theories......Page 380 1 Introduction......Page 381 2 Basic Equations......Page 383 3 Load and Metage......Page 384 4 Lagrangian variational principle of MHD......Page 388 5 Non Barotropic Cross Helicity Conservation via the Noether Theorem......Page 392 6 Conclusion......Page 394 References......Page 395 1 Introduction......Page 397 2 An Area-Dependent Potential......Page 398 3 Low-Lying Energy Spectrum......Page 399 4 Summary......Page 402 References......Page 404 1 Introduction......Page 405 2 Linear Nambu Flows for Classical and Quantum Magnets......Page 406 3 Computing Transition Probabilities la Nambu......Page 410 4 Conclusion and Outlook......Page 413 References......Page 414 1 Introduction......Page 415 2 Newton–Cartan Gravity Background......Page 417 3 Calculation of the Anomaly for Scalars and Fermions......Page 419 4 Conclusions......Page 420 References......Page 421 1 Introduction......Page 424 2 Time Evolution of a Free Non-relativistic Particle and a Particle in a Homogeneous Field......Page 425 3 Generalized Coherent States......Page 427 4 Unitary Equivalence for Oscillator-Like Solutions of a Free Non-relativistic Particle with Time-Dependent Mass and a Particle in a Time-Dependent Field......Page 431 References......Page 432 This book is the second volume of the proceedings of the joint conference X. International Symposium zQuantum Theory and Symmetriesy (QTS-X) and XII. International Workshop zLie Theory and Its Applications in Physicsy (LT-XII), 19-25 June 2017, Varna, Bulgaria. The QTS series started around the core concept that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium on the frontiers 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 facets of physics. As an interface between mathematics and physics the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In the division of the material between the two volumes, the Editor has tried to select for the first and second volumes papers that are more oriented toward mathematics and physics, respectively. However, this division is relative since many papers could have been placed in either volume. The topics covered in this volume represent the most modern trends in the fields of the joint conferences: symmetries in string theories, conformal field theory, holography, gravity theories and cosmology, gauge theories, foundations of quantum theory, nonrelativistic and classical theories