Quantum Field Theory on Curved Spacetimes

Concepts and Mathematical Foundations

  • Christian Bär
  • Klaus Fredenhagen

Part of the Lecture Notes in Physics book series (LNP, volume 786)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Christian Bär, Christian Becker
    Pages 1-37
  3. Frank Pfäffle
    Pages 39-58
  4. Nicolas Ginoux
    Pages 59-84
  5. Alexander Strohmaier
    Pages 85-127
  6. Romeo Brunetti, Klaus Fredenhagen
    Pages 129-155
  7. Back Matter
    Pages 1-4

About this book


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

Editors and affiliations

  • Christian Bär
    • 1
  • Klaus Fredenhagen
    • 2
  1. 1.Inst. MathematikUniversität PotsdamPotsdamGermany
  2. 2.Inst. Theoretische Physik IIUniversität HamburgHamburgGermany

Bibliographic information