Strong-coupling limits induced by weak-coupling expansions

IF 3 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
V.I. Yukalov , E.P. Yukalova
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引用次数: 0

Abstract

A method is described for the extrapolation of perturbative expansions in powers of asymptotically small coupling parameters or other variables onto the region of finite variables and even to the variables tending to infinity. The method involves the combination of ideas from renormalization group theory, approximation theory, dynamical theory, and optimal control theory. The extrapolation is realized by means of self-similar factor approximants, whose control parameters can be uniquely defined. The method allows to find the large-variable behavior of sought functions knowing only their small-variable expansions. Convergence and accuracy of the method are illustrated by explicit examples, including the so-called zero-dimensional field theory and anharmonic oscillator. Strong-coupling behavior of Gell-Mann–Low functions in multicomponent field theory, quantum electrodynamics, and quantum chromodynamics is found, being based on their weak-coupling perturbative expansions.

弱耦合扩展引起的强耦合极限
本文描述了一种方法,用于将渐近小耦合参数或其他变量幂的微扰展开外推到有限变量区域,甚至外推到趋于无穷大的变量区域。该方法结合了重正化群理论、近似理论、动力学理论和最优控制理论。外推法是通过自相似因子近似值实现的,其控制参数可以唯一定义。该方法只需知道所求函数的小变量展开,就能找到其大变量行为。该方法的收敛性和准确性通过明确的例子加以说明,包括所谓的零维场理论和非谐振荡器。在多分量场论、量子电动力学和量子色动力学中,基于盖尔-曼-洛函数的弱耦合微扰展开,发现了它们的强耦合行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Annals of Physics
Annals of Physics 物理-物理:综合
CiteScore
5.30
自引率
3.30%
发文量
211
审稿时长
47 days
期刊介绍: Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance. The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.
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