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Communications in Mathematical Physics

, Volume 237, Issue 1–2, pp 31–68 | Cite as

The Generally Covariant Locality Principle – A New Paradigm for Local Quantum Field Theory

  • Romeo Brunetti
  • Klaus Fredenhagen
  • Rainer Verch

Abstract:

 A new approach to the model-independent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity, thus giving rise to the concept of a locally covariant quantum field theory. Such locally covariant quantum field theories will be described mathematically in terms of covariant functors between the categories, on one side, of globally hyperbolic spacetimes with isometric embeddings as morphisms and, on the other side, of *-algebras with unital injective *-monomorphisms as morphisms. Moreover, locally covariant quantum fields can be described in this framework as natural transformations between certain functors. The usual Haag-Kastler framework of nets of operator-algebras over a fixed spacetime background-manifold, together with covariant automorphic actions of the isometry-group of the background spacetime, can be re-gained from this new approach as a special case. Examples of this new approach are also outlined. In case that a locally covariant quantum field theory obeys the time-slice axiom, one can naturally associate to it certain automorphic actions, called ``relative Cauchy-evolutions'', which describe the dynamical reaction of the quantum field theory to a local change of spacetime background metrics. The functional derivative of a relative Cauchy-evolution with respect to the spacetime metric is found to be a divergence-free quantity which has, as will be demonstrated in an example, the significance of an energy-momentum tensor (up to addition of scalar functions) for the locally covariant quantum field theory. Furthermore, we discuss the functorial properties of state spaces of locally covariant quantum field theories that entail the validity of the principle of local definiteness.

Keywords

Quantum Field Theory Natural Transformation Functional Derivative Isometric Embedding Covariant Functor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Romeo Brunetti
    • 1
  • Klaus Fredenhagen
    • 1
  • Rainer Verch
    • 2
  1. 1.II. Inst. f. Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany. E-mail: brunetti@na.infn.it; fredenha@x4u2.desy.deDE
  2. 2.Inst. f. Theoretische Physik, Universität Göttingen, Bunsenstrasse 9, 37073 Göttingen, Germany. E-mail: verch@theorie.physik.uni-goettingen.deDE

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