Quantum Field Theory and Gravity

1. Front Matter

   Pages i-xiv

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2. Quantum Gravity: Whence, Whither?

   • Claus Kiefer

   Pages 1-13

3. Local Covariance and Background Independence

   • Klaus Fredenhagen, Katarzyna Rejzner

   Pages 15-23

4. The “Big Wave” Theory for Dark Energy

   • Blake Temple

   Pages 25-40

5. Discrete and Continuum Third Quantization of Gravity

   • Steffen Gielen, Daniele Oriti

   Pages 41-64

6. Unsharp Values, Domains and Topoi

   • Andreas Döring, Rui Soares Barbosa

   Pages 65-96

7. Causal Boundary of Spacetimes:Revision and Applications to AdS/CFT Correspondence

   • José Luis Flores, Jónatan Herrera, Miguel Sánchez

   Pages 97-119

8. Some Mathematical Aspects of the Hawking Effect for Rotating Black Holes

   • Dietrich Häfner

   Pages 121-136

9. Observables in the General Boundary Formulation

   • Robert Oeckl

   Pages 137-156

10. Causal Fermion Systems: A Quantum Space-Time Emerging From an Action Principle

    • Felix Finster, Andreas Grotz, Daniela Schiefeneder

    Pages 157-182

11. CCR- versus CAR-Quantization on Curved Spacetimes

    • Christian Bär, Nicolas Ginoux

    Pages 183-206

12. On the Notion of ‘the Same Physics in All Spacetimes’

    • Christopher J. Fewster

    Pages 207-227

13. Local Covariance, Renormalization Ambiguity, and Local Thermal Equilibrium in Cosmology

    • Rainer Verch

    Pages 229-256

14. Shape Dynamics. An Introduction

    • Julian Barbour

    Pages 257-297

15. On the Motion of Point Defects in Relativistic Fields

    • Michael K.-H. Kiessling

    Pages 299-335

16. How Unique Are Higher-dimensional Black Holes?

    • Stefan Hollands

    Pages 337-344

17. Equivalence Principle, Quantum Mechanics, and Atom-Interferometric Tests

    • Domenico Giulini

    Pages 345-370

18. Back Matter

    Pages 371-380

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One of the most challenging problems of contemporary theoretical physics is the mathematically rigorous construction of a theory which describes gravitation and the other fundamental physical interactions within a common framework. The physical ideas which grew from attempts to develop such a theory require highly advanced mathematical methods and radically new physical concepts.

 

This book presents different approaches to a rigorous unified description of quantum fields and gravity. It contains a carefully selected cross-section of lively discussions which took place in autumn 2010 at the fifth conference "Quantum field theory and gravity - Conceptual and mathematical advances in the search for a unified framework" 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.

• category theory
• causal sets
• discrete space–time structures
• quantum gravity
• topoi

From the reviews:

“The articles present recent research on conceptual and mathematical issues aiming at a unified framework for quantum field theory and general relativity. … In my experience, this is the best single text to use to learn field theory that one can buy today. … for a solid grounding in the fundamentals of field theory there is no better place to start then this.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, March, 2014)

• , Lehrstuhl für Mathematik, Universität Regensburg, Regensburg, Germany

  Felix Finster, Olaf Müller

• , Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany

  Marc Nardmann

• in den Naturwissenschaften, Max-Planck-Institut für Mathematik, Leipzig, Germany

  Jürgen Tolksdorf, Eberhard Zeidler

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