123505431
Locally Covariant Quantum Field Theories
The generally covariant treatment of QFT discussed in this paper is based on the first principle that ensures equivalence of observable algebras based on isometric regions of different space-times. That’s all one needs to proceed, at the conceptual level. Important developments are those connected to the works of Hollands and Wald, Verch, Hollands, Ruzzi, and one easily foresees applications of the framework to interesting situations, such as those related to AdS space-time, or in general theories on space-times with boundaries, to the exploitation of the renormalization group at the algebraic level and its possible use towards a clarification of the role of the conformal anomaly in the treatment of theories on asymptotically AdS space-times. Another, perhaps more important topic, is that related to background independent formulation of perturbative quantum gravity. We hope to report on these soon.
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
14202736
Quantum Charges and Spacetime Topology: The Emergence of New Superselection Sectors
A new form of superselection sectors of topological origin is developed. By that it is meant a new investigation that includes several extensions of the traditional framework of Doplicher, Haag and Roberts in local quantum theories. At first we generalize the notion of representations of nets of C*–algebras, then we provide a brand new view on selection criteria by adopting one with a strong topological flavour. We prove that it is coherent with the older point of view, hence a clue to a genuine extension. In this light, we extend Roberts’ cohomological analysis to the case where 1–cocycles bear non-trivial unitary representations of the fundamental group of the spacetime, equivalently of its Cauchy surface in the case of global hyperbolicity. A crucial tool is a notion of group von Neumann algebras generated by the 1–cocycles evaluated on loops over fixed regions. One proves that these group von Neumann algebras are localized at the bounded region where loops start and end and to be factorial of finite type I. All that amounts to a new invariant, in a topological sense, which can be defined as the dimension of the factor. We prove that any 1–cocycle can be factorized into a part that contains only the charge content and another where only the topological information is stored. This second part much resembles what in literature is known as geometric phases. Indeed, by the very geometrical origin of the 1–cocycles that we discuss in the paper, they are essential tools in the theory of net bundles, and the topological part is related to their holonomy content. At the end we prove the existence of net representations.
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.
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