Related papers: Analytical continuation and resummed perturbation …
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 investigate the inversion of perturbation series and its resummation, and prove that it is related to a recently developed parametric perturbation theory. Results for some illustrative examples show that in some cases series reversion…
We present a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
This article aims to explain essential elements of perturbation theory and their conceptual underpinnings. It is not meant as a summary of popular perturbation methods, though some illustrative examples are given to underline the main…
A technique called analytic perturbation theory, which respects the required analytic properties, consistent with causality, is applied to the definition of the running coupling in the timelike region, to the description of inclusive…
The unitary transformation of path-integral differential measure is described. The main properties of perturbation theory in the phase space of action-angle, energy-time variables are investigated. The measure in cylindrical coordinates is…
An approach is suggested for analyzing time series by means of resummation techniques of theoretical physics. A particular form of such an analysis, based on the algebraic self-similar renormalization, is developed and illustrated by…
We give a general framework for the treatment of perturbations of types and structures in continuous logic, allowing to specify which parts of the logic may be perturbed. We prove that separable, elementarily equivalent structures which are…
The renormalization group applied to perturbation theory is ordinarily used to define the running coupling constant in the spacelike region. However, to describe processes with timelike momenta transfers, it is important to have a…
A perturbative approach for non renormalizable theories is developed. It is shown that the introduction of an extra expansion parameter allows one to get rid of divergences and express physical quantities as series with finite coefficients.…
We devise a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…
The improvement of resummation algorithms for divergent perturbative expansions in quantum field theory by asymptotic information about perturbative coefficients is investigated. Various asymptotically optimized resummation prescriptions…
A review of chiral perturbation theory and that of recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.
This short paper discusses continually updated causal abstractions as a potential direction of future research. The key idea is to revise the existing level of causal abstraction to a different level of detail that is both consistent with…
The dynamics of a system, made of a particle interacting with a field mode, thwarted by the action of repeated projective measurements on the particle, is examined. The effect of the partial measurements is discussed by comparing it with…
In the context of the inclusive $\tau$-decay, we analyze various forms of perturbative expansions which have appeared as modifications of the original perturbative series. We argue that analytic perturbation theory, which combines…
In this paper we provide a comprehensive study of statistical inference in linear and allied models which exhibit some analytic perturbations in their design and covariance matrices. We also indicate a few potential applications. In the…
The analysis of intermittent data is improved. The standard method of recovering the history of a particle cascade is proved in general not to reproduce the structure of the true cascade. The recovering corrections to the standard method…
The physical aspect of a general perturbation theory is explored. Its role as a physical principle for understanding the interaction among the matters with different levels of hierarchy is appreciated. It is shown that the general…