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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer Berlin Heidelberg

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DOI

10.1007/bf02196983

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1432-0916

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Phase Boundaries in Algebraic Conformal QFT

Authors: Marcel Bischoff Yasuyuki Kawahigashi Roberto Longo KarlHenning Rehren
Publish Date: 2016/01/21
Volume: 342, Issue: 1, Pages: 1-45
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Abstract

We study the structure of local algebras in relativistic conformal quantum field theory with phase boundaries Phase boundaries are instances of a more general notion of boundaries that give rise to a variety of algebraic structures These can be formulated in a common framework originating in Algebraic QFT with the principle of Einstein Causality playing a prominent role We classify the phase boundary conditions by the centre of a certain universal construction which produces a reducible representation in which all possible boundary conditions are realized For a large class of models the classification reproduces results obtained in a different approach by Fuchs et al beforeSupported in part by the ERC Advanced Grant 669240 QUEST “Quantum Algebraic Structures and Models” PRINMIUR GNAMPAINdAM and Alexander von Humboldt Foundation RL Supported by the GrantsinAid for Scientific Research JSPS YK Supported by the German Research Foundation Deutsche Forschungsgemeinschaft DFG through the Institutional Strategy of the University of Göttingen MB KHR The hospitality and support of the ErwinSchrödinger International Institute for Mathematical Physics Vienna is gratefully acknowledged

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  1. Statistics of Wave Functions for a Point Scatterer on the Torus
  2. Hausdorff Dimension of Julia Sets of Feigenbaum Polynomials with High Criticality
  3. Stability and Duality in $${\mathcal{N}\,{=}\,2}$$ Supergravity
  4. Exponential Mixing for the 3 D Stochastic Navier–Stokes Equations
  5. Binding of Polarons and Atoms at Threshold
  6. Probabilistic Weyl Laws for Quantized Tori
  7. On Perturbations of the Schwarzschild Anti-De Sitter Spaces of Positive Mass
  8. Wall-Crossing, Free Fermions and Crystal Melting
  9. Standing Ring Blow up Solutions to the N-Dimensional Quintic Nonlinear Schrödinger Equation
  10. Laminar Boundary Layers in Convective Heat Transport
  11. There are no Magnetically Charged Particle-like Solutions of the Einstein Yang-Mills Equations for Models with an Abelian Residual Group
  12. Duality of 2D Gravity as a Local Fourier Duality
  13. Nonlinear Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem with Degenerate Density Dependent Viscosities
  14. Extended Scaling Relations for Planar Lattice Models
  15. Infinite-Dimensional Schur–Weyl Duality and the Coxeter–Laplace Operator
  16. On the Singularity of the Free Energy at a First Order Phase Transition
  17. Free Analog of Pressure and Its Legendre Transform
  18. Continuity of the Lyapunov Exponents for Quasiperiodic Cocycles
  19. On the Correlation Function of the Characteristic Polynomials of the Hermitian Wigner Ensemble
  20. Stationary Random Metrics on Hierarchical Graphs Via $${(\min,+)}$$-type Recursive Distributional Equations
  21. Thermalization and Canonical Typicality in Translation-Invariant Quantum Lattice Systems
  22. Higgs Bundles and ( A , B , A )-Branes
  23. Inviscid Incompressible Limits of the Full Navier-Stokes-Fourier System
  24. Global Well-Posedness Issues for the Inviscid Boussinesq System with Yudovich’s Type Data
  25. Dispersive Estimates for Schrödinger Operators in Dimension Two
  26. A Monoidal Category for Perturbed Defects in Conformal Field Theory
  27. On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System
  28. Holomorphic Factorization for a Quantum Tetrahedron
  29. High Energy Limits of Laplace-Type and Dirac-Type EigenFunctions and Frame Flows
  30. The Operator Product Expansion for Perturbative Quantum Field Theory in Curved Spacetime
  31. The Szegő Kernel on a Sewn Riemann Surface
  32. Wave Relations
  33. An Application of Mirror Extensions
  34. Diffusion in a Weakly Random Hamiltonian Flow
  35. Spherical T-Duality
  36. A Fuchsian Matrix Differential Equation for Selberg Correlation Integrals
  37. Lax Pair Equations and Connes-Kreimer Renormalization
  38. SNA’s in the Quasi-Periodic Quadratic Family
  39. On the Geometry of Closed G 2 -Structures
  40. Irreducible Characters of General Linear Superalgebra and Super Duality
  41. Connecting Solutions of the Lorentz Force Equation do Exist
  42. Toric G 2 and Spin (7) Holonomy Spaces from Gravitational Instantons and Other Examples
  43. The Smoluchowski-Kramers Limit of Stochastic Differential Equations with Arbitrary State-Dependent Friction
  44. Dirac Reduction for Poisson Vertex Algebras
  45. Dispersive Estimates for Schrödinger Equations with Threshold Resonance and Eigenvalue
  46. Multipermutation Solutions of the Yang–Baxter Equation
  47. The Shape of Expansion Induced by a Line with Fast Diffusion in Fisher-KPP Equations
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  49. A Lower Bound on Blowup Rates for the 3D Incompressible Euler Equation and a Single Exponential Beale-Kato-Majda Type Estimate
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  51. Spin(7)-Instantons, Cayley Submanifolds and Fueter Sections
  52. Equivariant Comparison of Quantum Homogeneous Spaces
  53. Regular Strongly Typical Blocks of $${\mathcal{O}^{\mathfrak {q}}}$$
  54. Exponential Equations Related to the Quantum ‘ ax + b ’ Group
  55. Twisted Logarithmic Modules of Vertex Algebras
  56. Singular Continuous Spectrum for Singular Potentials
  57. How to Remove the Boundary in CFT – An Operator Algebraic Procedure
  58. Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles
  59. Multidimensional Continued Fractions, Dynamical Renormalization and KAM Theory
  60. Twistor Theory on a Finite Graph
  61. Triangular Invariants, Three-Point Functions and Particle Stability on the de Sitter Universe
  62. On positive functionals on algebras of test functions for quantum fields
  63. Large Deviations for the Yang-Mills Measure on a Compact Surface
  64. Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data
  65. Periodicity and the Determinant Bundle
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