Quantum Mathematical Physics

1. Front Matter

   Pages i-xiv

   PDF

2. On the Spin-Statistics Connection in Curved Spacetimes

   • Christopher J. Fewster

   Pages 1-18

3. Is There a C-Function in 4D Quantum Einstein Gravity?

   • Daniel Becker, Martin Reuter

   Pages 19-41

4. Systematic Renormalization at all Orders in the DiffRen and Improved Epstein–Glaser Schemes

   • José M. Gracia-Bondía

   Pages 43-53

5. Higgs Mechanism and Renormalization Group Flow: Are They Compatible?

   • Michael Dütsch

   Pages 55-76

6. Hadamard States From Null Infinity

   • Claudio Dappiaggi

   Pages 77-99

7. Local Thermal Equilibrium States in Relativistic Quantum Field Theory

   • Michael Gransee

   Pages 101-117

8. Categorical Methods in Quantum Field Theory

   • Frédéric Paugam

   Pages 119-135

9. A Solvable Four-Dimensional QFT

   • Harald Grosse, Raimar Wulkenhaar

   Pages 137-161

10. Wave Equations with Non-commutative Space and Time

    • Rainer Verch

    Pages 163-178

11. Thermal Equilibrium States for Quantum Fields on Non-commutative Spacetimes

    • Gandalf Lechner, Jan Schlemmer

    Pages 179-199

12. Kinematical Foundations of Loop Quantum Cosmology

    • Christian Fleischhack

    Pages 201-232

13. Cosmic Puzzles: Dark Matter and Dark Energy

    • Gerhard Börner

    Pages 233-255

14. Radiation and Scattering in Non-relativistic Quantum Electrodynamics

    • Israel Michael Sigal

    Pages 257-291

15. Avoiding Ultraviolet Divergence by Means of Interior–Boundary Conditions

    • Stefan Teufel, Roderich Tumulka

    Pages 293-311

16. Causal Fermion Systems: An Overview

    • Felix Finster

    Pages 313-380

17. A Perspective on External Field QED

    • Dirk-André Deckert, Franz Merkl

    Pages 381-399

18. Super Riemann Surfaces and the Super Conformal Action Functional

    • Enno Keßler

    Pages 401-419

19. Recent Developments in Deformation Quantization

    • Stefan Waldmann

    Pages 421-439

20. Dirac’s Point Electron in the Zero-Gravity Kerr–Newman World

    • Michael K.-H. Kiessling, A. Shadi Tahvildar-Zadeh

    Pages 441-469

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.

• general relativity
• quantum field theory
• mathematical physics
• quantum gravity
• quantum physics

• Universität Regensburg, Fakultät für Mathematik, Regensburg, Germany

  Felix Finster

• Regensburg, Germany, Fakultät für Mathematik Universität Rege, Regensburg, Germany

  Johannes Kleiner, Christian Röken

• Leipzig, Germany, MPI für Mathematik in den Naturwissensch, Leipzig, Germany

  Jürgen Tolksdorf

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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