We review the theory of quantum fields propagating in an arbitrary, classical, globally
hyperbolic spacetime. Our review emphasizes the conceptual issues arising in the …

We propose additional conditions (beyond those considered in our previous papers) that
should be imposed on Wick products and time-ordered products of a free quantum scalar …

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 …

We establish the existence of local, covariant time ordered products of local Wick
polynomials for a free scalar field in curved spacetime. Our time ordered products satisfy all …

On the one hand, perturbative quantum field theory (pQFT) is very successful: The results
obtained by computing the lowest orders of the perturbation series are in good agreement …

We present a proof that the quantum Yang–Mills theory can be consistently defined as a
renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved …

The perturbative treatment of quantum field theory is formulated within the framework of
algebraic quantum field theory. We show that the algebra of interacting fields is additive, ie …

We review in simple terms the covariant approaches to the canonical formulation of classical
relativistic field theories (in particular gauge field theories and general relativity) and we …

A bstract A non-perturbative and exactly solvable quantum field theoretical model for a
“dressed Dirac field” is presented, that exhibits all the kinematical features of QED: an …

We construct perturbative quantum gravity in a generally covariant way. In particular our
construction is background independent. It is based on the locally covariant approach to …