Algebraic dynamics in O*-algebras: a perturbative approach

TL;DR

This paper explores a perturbative method for recovering algebraic dynamics within O*-algebras of unbounded operators, providing conditions for the existence of dynamics as limits of regularized maps.

Contribution

It introduces a novel perturbative framework for algebraic dynamics in O*-algebras, focusing on unbounded operators and quasi-uniform topology.

Findings

Conditions established for the existence of dynamics as limits of regularized maps

Framework applicable to unbounded operator algebras in quantum physics

Provides a mathematical basis for perturbative analysis of algebraic dynamics

Abstract

In this paper the problem of recovering an algebraic dynamics in a perturbative approach is discussed. The mathematical environment in which the physical problem is considered is that of algebras of unbounded operators endowed with the quasi-uniform topology. After some remarks on the domain of the perturbation, conditions are given for the dynamics to exist as the limit of a net of regularized linear maps.