相关论文: Scaling Algebras and Renormalization Group in Alge…

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…

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)…

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 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.…

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…

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…

Short distance scaling limits of a class of integrable models on two-dimensional Minkowski space are considered in the algebraic framework of quantum field theory. Making use of the wedge-local quantum fields generating these models, it is…

We analyse a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R.…

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…

Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…

A simple theoretical model of scalar fields in one spatial dimension with internal symmetry is considered. Assuming the existence of localized classical field configurations, the Schr\"{o}dinger picture is used to describe their quantum…

It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics…

We develop the finite-size scaling (FSS) theory at quantum transitions, considering generic boundary conditions, such as open and periodic boundary conditions, and also the corrections to the leading FSS behaviors. Using…

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…

A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…

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…

Factorization algebras are local-to-global objects living on manifolds, and they arise naturally in mathematics and physics. Their local structure encompasses examples like associative algebras and vertex algebras; in these examples, their…

We investigate refined algebraic quantisation with group averaging in a finite-dimensional constrained Hamiltonian system that provides a simplified model of general relativity. The classical theory has gauge group SL(2,R) and a…

We introduced in a previous paper a general notion of asymptotic morphism of a given local net of observables, which allows to describe the sectors of a corresponding scaling limit net. Here, as an application, we illustrate the general…

If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime.…