Dyson–Schwinger equations in minimal subtraction

IF 1.5 Q2 PHYSICS, MATHEMATICAL Annales de l Institut Henri Poincare D Pub Date : 2021-09-28 DOI:10.4171/aihpd/169
Paul-Hermann Balduf
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引用次数: 4

Abstract

We compare the solutions of one-scale Dyson-Schwinger equations in the Minimal subtraction (MS) scheme to the solutions in kinematic (MOM) renormalization schemes. We establish that the MS-solution can be interpreted as a MOM-solution, but with a shifted renormalization point, where the shift itself is a function of the coupling. We derive relations between this shift and various renormalization group functions and counter terms in perturbation theory. As concrete examples, we examine three different one-scale Dyson-Schwinger equations, one based on the D=4 multiedge graph, one for the D=6 multiedge graph and one mathematical toy model. For each of the integral kernels, we examine both the linear and nine different non-linear Dyson-Schwinger equations. For the linear cases, we empirically find exact functional forms of the shift between MOM and MS renormalization points. For the non-linear DSEs, the results for the shift suggest a factorially divergent power series. We determine the leading asymptotic growth parameters and find them in agreement with the ones of the anomalous dimension. Finally, we present a tentative exact non-perturbative solution to one of the non-linear DSEs of the toy model.
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极小减法中的Dyson-Schwinger方程
我们比较了一尺度Dyson-Schwinger方程在最小减法(MS)格式下的解与运动(MOM)重整化格式下的解。我们建立了ms -解可以被解释为mom -解,但是具有移位的重整化点,其中移位本身是耦合的函数。导出了这种位移与微扰理论中各种重整化群函数和逆项之间的关系。作为具体的例子,我们研究了三种不同的单尺度Dyson-Schwinger方程,一种是基于D=4多边图的,一种是基于D=6多边图的,一种是数学玩具模型。对于每个积分核,我们检查了线性和九个不同的非线性Dyson-Schwinger方程。对于线性情况,我们经验地找到了MOM和MS重整化点之间位移的精确函数形式。对于非线性dse,位移的结果表明幂级数是阶乘发散的。我们确定了主要的渐近增长参数,并发现它们与异常维的渐近增长参数一致。最后,我们给出了一个玩具模型的非线性dse的暂定精确非摄动解。
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
16
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