Axiomatic quantum field theory in curved spacetime

The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features--such as Poincare invariance and the existence of a preferred vacuum state--that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is locally and covariantly constructed from the spacetime metric), a microlocal spectrum condition, an "associativity" condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of our new viewpoint on quantum field theory are discussed.Comment: Latex, 44 pages, 2 figure

Scaling algebras and pointlike fields: A nonperturbative approach to renormalization

We present a method of short-distance analysis in quantum field theory that does not require choosing a renormalization prescription a priori. We set out from a local net of algebras with associated pointlike quantum fields. The net has a naturally defined scaling limit in the sense of Buchholz and Verch; we investigate the effect of this limit on the pointlike fields. Both for the fields and their operator product expansions, a well-defined limit procedure can be established. This can always be interpreted in the usual sense of multiplicative renormalization, where the renormalization factors are determined by our analysis. We also consider the limits of symmetry actions. In particular, for suitable limit states, the group of scaling transformations induces a dilation symmetry in the limit theory.Comment: minor changes and clarifications; as to appear in Commun. Math. Phys.; 37 page

Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly1

Configuration (x-)space renormalization of euclidean Feynman amplitudes in a massless quantum field theory is reduced to the study of local extensions of associate homogeneous distributions. Primitively divergent graphs are renormalized, in particular, by subtracting the residue of an analytically regularized expression. Examples are given of computing residues that involve zeta values. The renormalized Green functions are again associate homogeneous distributions of the same degree that transform under indecomposable representations of the dilation group

A three-state model for the probability distribution of instantaneous solar radiation, with applications

Based on a new set of data covering a 13-month period and a wide range of the average clearness indices, the probability distribution for instantaneous solar radiation is modeled. The data's probability density function is shown to be capably represented by a linear superposition of three (truncated) normal distributions. The variable of the distribution is the "normalized clearness index", κ, which is the clearness index kt divided by its value under clear sky conditions—a quantity now available for most locations on the globe. It is shown that using κ as the variable makes the distribution independent of the air mass. The only other parameter in the distribution is the [mean value of κ]. The latter quantity fixes the parameters and the respective weights of the normal distributions, through empirically-derived fits. A physical interpretation of these findings is presented, whereby each normal distribution is associated with one of the three possible states of the atmosphere: namely (a) clear sky conditions, (b) overcast conditions, and (c) all other conditions. This interpretation predicts that the mean of the clear-sky state normal curve will be unity, and this has been confirmed for the data in hand. Also lending support to the three-state interpretation, is its ability (demonstrated in this paper) to predict the fraction of time of bright sunshine. Based on this new three-state model, a preliminary first-principle model for the mean diffuse fraction is given, as well as expressions for mean radiation on inclined surfaces and the instantaneous utilizability. The instantaneous utilizability is found to be greater than that for hourly or daily time periods and to depend in a significant way on the clear sky value of kt