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

We present a new viewpoint on the construction of pointlike local fields in integrable models of quantum field theory. As usual, we define these local observables by their form factors; but rather than exhibiting their $n$-point functions…

We carry out the complete group classification of the class of (1+1)-dimensional linear Schr\"odinger equations with complex-valued potentials. After introducing the notion of uniformly semi-normalized classes of differential equations, we…

A system of stochastic differential equations for the velocity and density of a classical self-gravitating matter is investigated by means of the field theoretic renormalization group. The existence of two types of large-scale scaling…

The kinematical foundations of Schwinger's algebra of selective measurements were discussed in a previous paper (arXiv:1905.12274) and, as a consequence of this, a new picture of quantum mechanics based on groupoids was proposed. In this…

We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale…

We approach the study of non--integrable models of two--dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact $S$-matrix and Form Factors of the integrable field theories we…

There has been much recent interest in the necessity of an observer degree of freedom in the description of local algebras in semiclassical gravity. In this work, we describe an example where the observer can be constructed intrinsically…

Within the framework of the universal algebra of the electromagnetic field, the impact of globally neutral configurations of external charges on the field is analyzed. External charges are not affected by the field, but they induce…

In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding…

The 1/N expansion in quantum field theory is formulated within an algebraic framework. For a scalar field taking values in the $N$ by $N$ hermitian matrices, we rigorously construct the gauge invariant interacting quantum field operators in…

Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…

Quantum electrodynamics in $1+1$ dimensions (Schwinger model) on an interval admits lattice discretization with a finite-dimensional Hilbert space, and is often used as a testbed for quantum and tensor network simulations. In this work we…

Quantum theories of gravity are generally expected to have some degree of non-locality, with familiar local physics emerging only in a particular limit. Perturbative quantum gravity around backgrounds with isometries and compact Cauchy…

A new formalism for the perturbative construction of algebraic quantum field theory is developed. The formalism allows the treatment of low dimensional theories and of non-polynomial interactions. We discuss the connection between the…

Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…

Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…

Symmetry algebras deriving from towers of soft theorems can be deformed by a short list of higher-dimension Wilsonian corrections to the effective action. We study the simplest of these deformations in gauge theory arising from a massless…

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.…

Several issues in the modal approach to quantum field theory are discussed. Within the formalism of spherical field theory, differential renormalization is presented and shown to result in a finite number of renormalization parameters.…

A reparametrization invariant model, introduced by Montesinos, Rovelli and Thiemann, possessing an SL(2,R) gauge symmetry is treated along the guidelines of an algebraic constraint quantization scheme that translates the vanishing of the…