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Quantum Mathematical Physics

A Bridge between Mathematics and Physics

  • Book
  • © 2016

Overview

Editors:
  1. Felix Finster

    1. Universität Regensburg, Fakultät für Mathematik, Regensburg, Germany

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  2. Johannes Kleiner

    1. Regensburg, Germany, Fakultät für Mathematik Universität Rege, Regensburg, Germany

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  3. Christian Röken

    1. Regensburg, Germany, Fakultät für Mathematik Universität Rege, Regensburg, Germany

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  4. Jürgen Tolksdorf

    1. Leipzig, Germany, MPI für Mathematik in den Naturwissensch, Leipzig, Germany

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  • Contributions from internationally recognized researchers in mathematics and physics
  • This book presents different physical ideas and mathematical approaches
  • This volume contains a carefully selected cross-section of lectures

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xiv
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  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
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Keywords

About this book

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.


Editors and Affiliations

  • 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

About the editors

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.

Bibliographic Information

  • Book Title: Quantum Mathematical Physics

  • Book Subtitle: A Bridge between Mathematics and Physics

  • Editors: Felix Finster, Johannes Kleiner, Christian Röken, Jürgen Tolksdorf

  • DOI: https://doi.org/10.1007/978-3-319-26902-3

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-26900-9Published: 04 March 2016

  • Softcover ISBN: 978-3-319-80039-4Published: 07 April 2018

  • eBook ISBN: 978-3-319-26902-3Published: 24 February 2016

  • Edition Number: 1

  • Number of Pages: XIV, 518

  • Number of Illustrations: 20 b/w illustrations, 18 illustrations in colour

  • Topics: Mathematical Physics, Theoretical, Mathematical and Computational Physics

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