Quantum Mathematical Physics: A Bridge between Mathematics and Physics

Felix Finster, Johannes Kleiner, Christian Röken, Jürgen Tolksdorf
Birkhäuser, 24 févr. 2016 - 518 pages
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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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Table des matières

Systematic Renormalization at all Orders in the DiffRen and Improved EpsteinGlaser Schemes
Are They Compatible?
Hadamard States From Null Infinity
Local Thermal Equilibrium States in Relativistic Quantum Field Theory
Categorical Methods in Quantum Field Theory
A Solvable FourDimensional QFT
Wave Equations with Noncommutative Space and Time
Thermal Equilibrium States for Quantum Fields on Noncommutative Spacetimes
Avoiding Ultraviolet Divergence by Means of InteriorBoundary Conditions
An Overview
A Perspective on External Field QED
Super Riemann Surfaces and the Super Conformal Action Functional
Recent Developments in Deformation Quantization
Diracs Point Electron in the ZeroGravity KerrNewman World
Noncommutative Geometry and the Physics of the LHC Era
Variational Stability and Rigidity of Compact Einstein Manifolds

Kinematical Foundations of Loop Quantum Cosmology
Dark Matter and Dark Energy
Radiation and Scattering in Nonrelativistic QuantumElectrodynamics

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À propos de l'auteur (2016)

Felix Finster Professor of Mathematics at the University of Regensburg working mainly on mathematical problems in general relativity and quantum theory. Jürgen Tolksdorf is Privatdozent in Mathematics at the Max-Planck-Institute for Mathematics in the Sciences in Leipzig. Eberhard Zeidler was Director at the Max-Planck-Institute for Mathematics in the Sciences in Leipzig and is Honorary Professor of Mathematics at the University of Leipzig.

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