119669414
The Generally Covariant Locality Principle – A New Paradigm for Local Quantum Field Theory
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.
126029541
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15566788
A remark on alpha vacua for quantum field theories on de Sitter space
It is shown that the so-called α-vacua which have been proposed as candidates for states of free quantum fields on de Sitter space have infinitely strong fluctuations for typical observables as the averaged renormalized energy momentum tensor.
16304913
Interacting Quantum Fields on a Curved Background
A renormalized perturbative expansion of interacting quantum fields on a globally hyperbolic spacetime is performed by adapting the Bogoliubov Epstein Glaser method to a curved background. The results heavily rely on techniques from microlocal analysis, in particular on Radzikowski’s characterization of Hadamard states by wave front sets of Wightman functions. Quantum field theory on a curved background is supposed to describe correctly the influence of a gravitational field on quantum fields as long as the relevant length scales are much larger than the Planck length. The modifications compared to quantum field theory on Minkowski space are mainly due to some nonlocal features in the standard formulation of quantum field theory. The most important ones are the spectrum condition and the existence of a vacuum, properties expressing stability of the system and, on a more technical side, making possible the transition to a euclidean formulation. Even for free fields the changes are by no means trivial, leading to new phenomena as e.g. the Hawking radiation of black holes. It seems now to be clear that the notion of a vacuum has to be replaced by the choice of a class of admissable states [1] which was identified to be the class of Hadamard states [2, 3, 4]. Accordingly, also the Feynman propagator is no longer unique, but its singular part is fixed and has essentially the same form as on Minkowski space. Therefore the ultraviolet divergences of perturbation theory should be treatable and should be similar to those in Minkowski space. This expectation fits with the results
8325525
Quantum Field Theory on Curved Backgrounds
Quantum field theory is an extremely successful piece of theoretical physics. Based on few general principles, it describes with an incredibly good precision large parts of particle physics. But also in other fields, in particular in solid state physics, it yields important applications. At present, the only problem which seems to go beyond the general framework of quantum field theory is the incorporation of gravity. Quantum field theory on curved backgrounds aims at a step toward solving this problem by neglecting the back reaction of the quantum fields on the spacetime metric.
16950827
General covariance in algebraic quantum field theory.
In this review we report on how the problem of general covariance is treated within the algebraic approach to quantum field theory by use of concepts from category theory. Some new results on net cohomology and superselection structure attained in this framework are included.
10960976
A web-based utility for Grid data management