The Generally Covariant Locality Principle  A New Paradigm for Local Quantum Field Theory
Abstract
A new approach to the modelindependent 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 HaagKastler framework of nets of operatoralgebras over a fixed spacetime backgroundmanifold, together with covariant automorphic actions of the isometrygroup of the background spacetime, can be regained 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 timeslice axiom, one can naturally associate to it certain automorphic actions, called ``relative Cauchyevolutions'', which describe the dynamical reaction of the quantum field theory to a local change of spacetime background metrics. The functional derivative of a relative Cauchyevolution with respect to the spacetime metric is found to be a divergencefree quantity which has, as will be demonstrated in an example, the significance of an energymomentum 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2003
 DOI:
 10.1007/s0022000308157
 arXiv:
 arXiv:mathph/0112041
 Bibcode:
 2003CMaPh.237...31B
 Keywords:

 Mathematical Physics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 latex2e, 34 p