7342713
Superselection Sectors and General Covariance. I
This paper is devoted to the analysis of charged superselection sectors in the framework of the locally covariant quantum field theories. We shall analyze sharply localizable charges, and use net-cohomology of J.E. Roberts as a main tool. We show that to any 4-dimensional globally hyperbolic spacetime a unique, up to equivalence, symmetric tensor $${\mathrm{C}^*}$$ -category with conjugates (in case of finite statistics) is attached; to any embedding between different spacetimes, the corresponding categories can be embedded, contravariantly, in such a way that all the charged quantum numbers of sectors are preserved. This entails that to any spacetime is associated a unique gauge group, up to isomorphisms, and that to any embedding between two spacetimes there corresponds a group morphism between the related gauge groups. This form of covariance between sectors also brings to light the issue whether local and global sectors are the same. We conjecture this holds that at least on simply connected spacetimes. It is argued that the possible failure might be related to the presence of topological charges. Our analysis seems to describe theories which have a well defined short-distance asymptotic behaviour.
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
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.
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.
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.
126029541
When does a detector click
10960976
A web-based utility for Grid data management