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.
119018200
Algebraic approach to Quantum Field Theory
We provide a short introduction to the main features of the algebraic approach to quantum field theories.
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.
85497753
Algebraic Structure of Classical Field Theory: Kinematics and Linearized Dynamics for Real Scalar Fields
We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field theory. This approach is local and focuses mainly on the observables over field configurations, given by certain spaces of functionals which are studied here in depth. The analysis of such functionals is characterized by a combination of geometric, analytic and algebraic elements which (1) make our approach closer to quantum field theory, (2) allow for a rigorous analytic refinement of many computational formulae from the functional formulation of classical field theory and (3) provide a new pathway towards understanding dynamics. Particular attention will be paid to aspects related to nonlinear hyperbolic partial differential equations and their linearizations.
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
8124566
Group cohomology, modular theory and space-time symmetries
The Bisognano-Wichmann property on the geometric behavior of the modular group of the von Neumann algebras of local observables associated to wedge regions in Quantum Field Theory is shown to provide an intrinsic sufficient criterion for the existence of a covariant action of the (universal covering of) the Poincare group. In particular this gives, together with our previous results, an intrinsic characterization of positive-energy conformal pre-cosheaves of von Neumann algebras. To this end we adapt to our use Moore theory of central extensions of locally compact groups by polish groups, selecting and making an analysis of a wider class of extensions with natural measurable properties and showing henceforth that the universal covering of the Poincare group has only trivial central extensions (vanishing of the first and second order cohomology) within our class.
10960976
A web-based utility for Grid data management