Related papers: Three Etudes in QFT
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection…
A review of the Hodge and Hopf-algebraic approach to QFT.
The structure of the QFT expansion is studied in the framework of a new "Invariant analytic" version of the perturbative QCD. Here, an invariant (running) coupling $a(Q^2/\Lambda^2)=\beta_1\alpha_s(Q^2)/4\pi$ is transformed into a…
We review recent results on the existence of asymptotic observables in algebraic QFT. The problem of asymptotic completeness is discussed from this perspective.
We demonstrate that perturbative algebraic QFT methods, as developed by Fredenhagen and Rejzner, naturally yields a factorization algebras of observables for a large class of Lorentzian theories. Along the way we carefully articulate…
We summarize the current status of our understanding of the structure of the perturbative QCD expressions for the QCD generalization of the Crewther relation.
We review the basic aspects of the perturbative QCD based on the operator product expansion to analyze the nucleon structure functions in a pedagogical way. We explain the non-trivial relation between the QCD results and the parton model…
In this review, we summarize the main ideas of perturbative algebraic quantum field theory, which is a rigorous framework combining some of the Haag-Kastler axioms with perturbative methods involving formal power series. It allows for the…
We employ the recently discovered Hopf algebra structure underlying perturbative Quantum Field Theory to derive iterated integral representations for Feynman diagrams. We give two applications: to massless Yukawa theory and quantum…
Two new approaches to numerical QFT are presented.
In this talk we review recent perturbative and non-perturbative developments in Heavy Quark Effective Theory (HQET).
Here, we report briefly two topics: 1) The latest version of ``Analytic Perturbation Theory" (APT) devised recently for the QCD observables both in the Euclidean and Minkowskian regions. 2) Results of the APT--based calculation for some…
We give an overview over several constructions of TQFT's over finite fields and cyclotomic integers and their applications to characterizing 3-manifolds and their fundamental groups.
Revisiting the old problem of existence of interacting models of QFT with new conceptual ideas and mathematical tools, one arrives at a novel view about the nature of QFT. The recent success of algebraic methods in establishing the…
Perturbation expansions appear to be divergent series in many physically interesting situations, including in quantum field theories like quantum electrodynamics (QED) and quantum chromodynamics (QCD), where the perturbative coefficients…
In this paper we give a streamlined overview of some of the recent constructions provided with K.-H. Neeb, G. \'Olafsson and collaborators for a new geometric approach to Algebraic Quantum Field Theory (AQFT). Motivations, fundamental…
In this report I review some aspects of the algebraic structure of QFT related with the doubling of the degrees of freedom of the system under study. I show how such a doubling is related to the characterizing feature of QFT consisting in…
In this talk, I review recent developments in perturbative QCD and their applications to collider physics.
We review the construction of models of algebraic quantum field theory by renormalized perturbation theory.
The content of this paper is incorporated into hep-th/9805093