Related papers: Scaling algebras and pointlike fields: A nonpertur…
For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary…
We summarize the new scaling algebra approach to the structural analysis of the short distance behaviour of quantum field theories in the operator algebraic formulation which has recently been proposed by D. Buchholz, R. Verch (Rev. Math.…
The concept of scaling algebra provides a novel framework for the general structural analysis and classification of the short distance properties of algebras of local observables in relativistic quantum field theory. In the present article…
The method of scaling algebras, which has been introduced earlier as a means for analyzing the short-distance behaviour of quantum field theories in the setting of the model-independent, operator-algebraic approach, is extended to the case…
We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…
The asymptotic high momentum behaviour of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x << 1. Particular emphasis is paid to theories with interactions…
Recently D. Buchholz and R. Verch have proposed a method for implementing in algebraic quantum field theory ideas from renormalization group analysis of short-distance (high energy) behavior by passing to certain scaling limit theories.…
For any given algebra of local observables in relativistic quantum field theory there exists an associated scaling algebra which permits one to introduce renormalization group transformations and to construct the scaling (short distance)…
It is well known that a minimal distance emerges in quantum field theories owing to the need to regularize the UV divergences. The macroscopical limit at large minimal distance, weak spatial resolution, is investigated for a self…
Renormalization is a powerful technique in statistical physics to extract the large-scale behavior of interacting many-body models. These notes aim to give an introduction to perturbative methods that operate on the level of the stochastic…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
Within the framework of algebraic quantum field theory a general method is presented which allows one to compute and classify the short distance (scaling) limit of any algebra of local observables. The results can be used to determine the…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
Using the machinery of smooth scaling and coarse-graining of observables, developed recently in the context of so-called fluctuation operators (originally developed by Verbeure et al), we extend this approach to a rigorous renormalisation…
A perturbative renormalization group method is used to obtain steady-state density profiles of a particle non-conserving asymmetric simple exclusion process. This method allows us to obtain a globally valid solution for the density profile…
The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of…
We report on a rigorous operator-algebraic renormalization group scheme and construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the…
We present a rigorous renormalization group scheme for lattice quantum field theories in terms of operator algebras. The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We construct…
We study the information content of the reduced density matrix of a region in quantum field theory that cannot be recovered from its subregion density matrices. We reconstruct the density matrix from its subregions using two approaches:…
We review the techniques used to renormalize quantum field theories at several loop orders. This includes the techniques to systematically extract the infinities in a Feynman integral and the implementation of the algorithm within computer…