量子场论中的自相似外推
Self-similar extrapolation in quantum field theory
摘要：
场论中的计算通常是通过使用微扰理论的某些变体来完成的，例如使用回路展开。这些计算结果在小耦合参数，作为一项规则是发散的参数的有限值的幂的渐近级数。在本文中，描述了一种方法，允许外推这种渐近级数的耦合参数的有限值，甚至其无限的限制。该方法是基于自相似近似理论。这个理论很好地近似了一大类函数，有理函数、无理函数和先验函数。提出了一种方法，导致自相似因子逼近允许外推的功能，耦合参数的任意值，只有知识的权力小耦合参数的扩展。用量子场论的几个问题说明了该方法的有效性。
英文摘要：
Calculations in field theory are usually accomplished by employing some variants of perturbation theory, for instance using loop expansions. These calculations result in asymptotic series in powers of small coupling parameters, which as a rule are divergent for finite values of the parameters. In this paper, a method is described allowing for the extrapolation of such asymptotic series to finite values of the coupling parameters, and even to their infinite limits. The method is based on self-similar approximation theory. This theory approximates well a large class of functions, rational, irrational, and transcendental. A method is presented, resulting in self-similar factor approximants allowing for the extrapolation of functions to arbitrary values of coupling parameters from only the knowledge of expansions in powers of small coupling parameters. The efficiency of the method is illustrated by several problems of quantum field theory.
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