## Quantum Mathematical Physics: A Bridge between Mathematics and PhysicsFelix Finster, Johannes Kleiner, Christian Röken, Jürgen Tolksdorf Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area. |

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### Contents

Systematic Renormalization at all Orders in the DiffRen and Improved EpsteinGlaser Schemes | 43 |

Are They Compatible? | 54 |

Hadamard States From Null Infinity | 77 |

Local Thermal Equilibrium States in Relativistic Quantum Field Theory | 101 |

Categorical Methods in Quantum Field Theory | 118 |

A Solvable FourDimensional QFT | 137 |

Wave Equations with Noncommutative Space and Time | 162 |

Thermal Equilibrium States for Quantum Fields on Noncommutative Spacetimes | 179 |

Avoiding Ultraviolet Divergence by Means of InteriorBoundary Conditions | 293 |

An Overview | 312 |

A Perspective on External Field QED | 381 |

Super Riemann Surfaces and the Super Conformal Action Functional | 401 |

Recent Developments in Deformation Quantization | 420 |

Diracs Point Electron in the ZeroGravity KerrNewman World | 441 |

Noncommutative Geometry and the Physics of the LHC Era | 470 |

Variational Stability and Rigidity of Compact Einstein Manifolds | 497 |

### Other editions - View all

Quantum Mathematical Physics: A Bridge Between Mathematics and Physics Felix Finster,Johannes Kleiner,Christian Roken No preview available - 2018 |

### Common terms and phrases

ˇ ˇ action functional algebra analytic asymptotically bosonic bundle Cauchy surface causal fermion system classical commutative compact configuration space constant construction corresponding cosmological covariant defined definition deformation quantization denotes derived diffeomorphism Dirac equation Dirac operator Dirac sea dynamics eigenvalues Einstein electron energy fermion fermionic projector finite Finster Fock space functor gauge geometry given globally hyperbolic Hadamard Hamiltonian Hilbert space integral interaction invariant isomorphism kernel linear loop quantum loop quantum cosmology Lorentzian spectral manifold mass Math matrix measure metric Minkowski space Minkowski spacetime morphisms noncommutative parameter particle perturbation photon Phys Poisson properties quantum field theory quantum gravity renormalization representation Riemann surfaces scalar field scale Sect smooth solution spacelike spectral triple spectrum spin spinor standard model star products structure subspace super Riemann surfaces symmetry tensor Theorem thermal topology transformation unitary vacuum vector wave functions Weyl