Finster F., Kleiner J. Rӧken C., Tolksdorf J. (Eds.) Quantum Mathematical Physics: A Bridge between Mathematics and Physics

Springer International Publishing Switzerland, 2016. – 518 p. – ISBN10: 3319269003.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
Topics
Mathematical Physics
Theoretical, Mathematical and Computational PhysicsOn the Spin-Statistics Connection in Curved Spacetimes
Is There a C-Function in 4D Quantum Einstein Gravity?
Systematic Renormalization at all Orders in the DiffRen and Improved Epstein–Glaser Schemes
Higgs Mechanism and Renormalization Group Flow: Are They Compatible?
Hadamard States From Null Infinity
Local Thermal Equilibrium States in Relativistic Quantum Field Theory
CategoricalMethods in Quantum Field Theory
A Solvable Four-Dimensional QFT
Wave Equations with Non-commutative Space and Time
Thermal Equilibrium States for Quantum Fields on Non-commutative Spacetimes
Kinematical Foundations of Loop Quantum Cosmology
Cosmic Puzzles: Dark Matter and Dark Energy
Radiation and Scattering in Non-relativistic Quantum Electrodynamics
Avoiding Ultraviolet Divergence by Means of Interior–Boundary Conditions
Causal Fermion Systems: An Overview
A Perspective on External Field QED
Super Riemann Surfaces and the Super Conformal Action Functional
Recent Developments in Deformation Quantization
Dirac’s Point Electron in the Zero-Gravity Kerr–NewmanWorld
Noncommutative Geometry and the Physics of the LHC Era
Variational Stability and Rigidity of Compact Einstein Manifolds