[en] We present a perturbative construction of interacting quantum field theories on smooth globally hyperbolic (curved) space-times. We develop a purely local version of the Stueckelberg-Bogoliubov-Epstein-Glaser method of renormalization by using techniques from microlocal analysis. Relying on recent results of Radzikowski, Koehler and the authors about a formulation of a local spectrum condition in terms of wave front sets of correlation functions of quantum fields on curved space-times, we construct time-ordered operator-valued products of Wick polynomials of free fields. They serve as building blocks for a local (perturbative) definition of interacting fields. Renormalization in this framework amounts to extensions of expectation values of time-ordered products to all points of space-time. The extensions are classified according to a microlocal generalization of Steinmann scaling degree corresponding to the degree of divergence in other renormalization schemes. As a result, we prove that the usual perturbative classification of interacting quantum field theories holds also on curved space-times. Finite renormalizations are deferred to a subsequent paper. As byproducts, we describe a perturbative construction of local algebras of observables, present a new definition of Wick polynomials as operator-valued distributions on a natural domain, and we find a general method for the extension of distributions which were defined on the complement of some surface. (orig.)

[en] The general framework of Algebraic Quantum Field Theory may be described as a covariant functor between two categories. The first one contains the information on local relations and is crucial for the interpretation. Its objects are topological spaces with additional structures (typically globally hyperbolic Lorentzian spaces, possibly spin bundles with connections, etc.), its morphisms structure preserving embeddings. In the case of globally hyperbolic Lorentzian spacetimes one requires that the embeddings are isometric and preserve the causal structure. The second category describes the algebraic structure of observables, in quantum physics the standard assumption is that one deals with the category of C*-algebras where the morphisms are unital embeddings. In classical physics one looks instead at Poisson algebras, and in perturbative quantum field theory one admits algebras which possess nontrivial representations as formal power series of Hilbert space operators. It is the leading principle of Algebraic Quantum Field Theory that the functor A contains all physical information. In particular, two theories are equivalent if the corresponding functors are naturally equivalent. In the analysis of the functor A a crucial role is played by natural transformations from other functors on the locality category. For instance, a field A may be defined as a natural transformation from the category of test function spaces to the category of observable algebras via their functors related to the locality category. (orig.)

[en] We propose a general construction of an observable measuring the time of occurence of an effect in quantum theory. Time delay in potential scattering theory is computed as a straightforward application. (orig.)

No abstract available

[en] 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. (orig.)

[en] In a typical scientific computing centre, diverse applications coexist and share a single physical infrastructure. An underlying Private Cloud facility eases the management and maintenance of heterogeneous use cases such as multipurpose or application-specific batch farms, Grid sites catering to different communities, parallel interactive data analysis facilities and others. It allows to dynamically and efficiently allocate resources to any application and to tailor the virtual machines according to the applications' requirements. Furthermore, the maintenance of large deployments of complex and rapidly evolving middleware and application software is eased by the use of virtual images and contextualization techniques; for example, rolling updates can be performed easily and minimizing the downtime. In this contribution we describe the Private Cloud infrastructure at the INFN-Torino Computer Centre, that hosts a full-fledged WLCG Tier-2 site and a dynamically expandable PROOF-based Interactive Analysis Facility for the ALICE experiment at the CERN LHC and several smaller scientific computing applications. The Private Cloud building blocks include the OpenNebula software stack, the GlusterFS filesystem (used in two different configurations for worker- and service-class hypervisors) and the OpenWRT Linux distribution (used for network virtualization). A future integration into a federated higher-level infrastructure is made possible by exposing commonly used APIs like EC2 and by using mainstream contextualization tools like CloudInit.

[en] Quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis. We discuss a condition on the wave front set for the corresponding n-point distributions, called ''microlocal spectrum condition'' (μSC). On Minkowski space, this condition is satisfied as a consequence of the usual spectrum condition. Based on Radzikowski's determination of the wave front set of the two point function of a free scalar field, satisfying the Hadamard condition in the Kay and Wald sense, we construct in the second part of this paper all Wick polynomials including the energy-momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our ''microlocal spectrum condition.'' (orig.). With 2 figs

[en] Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories, i.e. the Tomita-Takesaki modular group associated with the von Neumann algebra of a wedge region and vacuum vector coincides with the evolution given by the rescaled pure Lorentz transformations preserving the wedge. A similar geometric description is valid for the algebras associated with double cones. Moreover essential duality holds on the Minkowski space M, and Haag duality for double cones holds provided the net of local algebras is extended to a pre-cosheaf on the superworld anti M, i.e. the universal covering of the Dirac-Weyl compactification of M. As a consequence a PCT symmetry exists for any algebraic conformal field theory in even spacetime dimension. Analogous results hold for a Poincare covariant theory provided the modular groups corresponding to wedge algebras have the expected geometrical meaning and the split property is satisfied. In particular the Poincare representation is unique in this case. (orig.)

[en] 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 *-endomorphisms 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 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. (orig.)

[en] We propose a general construction of an observable measuring the time of occurrence of an effect in quantum theory. Time delay in potential scattering theory is computed as a straightforward application