Quantum Field Theory on Curved Spacetimes

1. Front Matter

   Pages i-ix

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2. C*-algebras

   • Christian Bär, Christian Becker

   Pages 1-37

3. Lorentzian Manifolds

   • Frank Pfäffle

   Pages 39-58

4. Linear Wave Equations

   • Nicolas Ginoux

   Pages 59-84

5. Microlocal Analysis

   • Alexander Strohmaier

   Pages 85-127

6. Quantum Field Theory on Curved Backgrounds

   • Romeo Brunetti, Klaus Fredenhagen

   Pages 129-155

7. Back Matter

   Pages 157-160

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After some decades of work a satisfactory theory of quantum gravity is still not available; moreover, there are indications that the original field theoretical approach may be better suited than originally expected. There, to first approximation, one is left with the problem of quantum field theory on Lorentzian manifolds. Surprisingly, this seemingly modest approach leads to far reaching conceptual and mathematical problems and to spectacular predictions, the most famous one being the Hawking radiation of black holes. Ingredients of this approach are the formulation of quantum physics in terms of C*-algebras, the geometry of Lorentzian manifolds, in particular their causal structure, and linear hyperbolic differential equations where the well-posedness of the Cauchy problem plays a distinguished role, as well as more recently the insights from suitable concepts such as microlocal analysis. This primer is an outgrowth of a compact course given by the editors and contributing authors to an audience of advanced graduate students and young researchers in the field, and assumes working knowledge of differential geometry and functional analysis on the part of the reader.

• C* algebras
• Gravity
• Lorentzian manifolds
• differential geometry
• manifold
• microlocal analysis
• quantum field theory
• quantum gravity

From the reviews:

“This is a very nice book which captures in only 160 pages the most important aspects of the mathematical and conceptional foundations of quantum field theory on curved spacetimes. … the interested reader can find here an introduction to the key concepts and pointers towards further literature. I can recommend this book to readers who are new to the subject as an ideal starting point, and also to more experienced researchers who are looking for a short and concise overview.” (Michael Keyl, Mathematical Reviews, Issue 2011 f)

• Inst. Mathematik, Universität Potsdam, Potsdam, Germany

  Christian Bär

• Inst. Theoretische Physik II, Universität Hamburg, Hamburg, Germany

  Klaus Fredenhagen

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