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第519行：
第519行： − 如图3所示，将反项的交互顶点放置在图3中的图抵消了图2中与循环的发散。+ 第527行：
第527行： − 从历史上看，将“无条件术语”分解为原始术语和对位术语的做法，早于肯尼思 · 威尔逊对重整化群的洞察力。根据这些重整化群的见解，这种分裂是非自然的，实际上是非物理的，因为问题的所有尺度都是以连续的系统方式进入的。+ 第537行：
第537行： − 为了尽量减少环路图对给定计算的贡献(从而使得计算结果更容易提取) ，我们选择一个重整化点接近相互作用中交换的能量和动量。然而，重整化点本身并不是一个物理量: 理论的物理预测，计算到所有的阶，原则上应该独立于重整化点的选择，只要它在理论的应用范围内。重整化尺度的变化将简单地影响有多少结果来自没有循环的费曼图，有多少结果来自循环图剩余的有限部分。人们可以利用这一事实来计算物理常数随规模变化的有效变化。这种变化是由 β 函数编码的，这种尺度依赖的一般理论被称为重整化群。+ 第545行：
第545行： − 通俗地说，粒子物理学家经常说某些物理“常数”随着相互作用的能量而变化，尽管事实上，重整化标度才是独立量。然而，这种运行确实提供了一种方便的手段来描述场理论在相互作用所涉及的能量变化下的行为变化。例如，由于量子色动力学中的耦合在大能量尺度下变小，该理论表现得更像一个自由理论，因为在相互作用中交换的能量变大了---- 这种现象被称为渐近自由。选择一个递增的能量尺度并使用重整化群，可以从简单的费曼图中清楚地看出这一点; 如果不这样做，预测结果将是一样的，但是会出现复杂的高阶取消。+ 第561行：
第561行： − + 第577行：
第577行： − 为了消除散度，只需将积分的下限改为和:+ 第585行：
第585行： − “ i = ln a-ln b-ln { varepsilon _ a } + ln { varepsilon _ b } = ln tfrac { a }{ b }-ln varepsilon _ a }{ varepsilon _ b } </math > + 第593行：
第593行： − 确保→1} ，然后 ln. }}+
第三小节Renormalized and bare quantities内容完成翻译矫正
The diagram with the counterterm's interaction vertex placed as in Figure 3 cancels out the divergence from the loop in Figure 2.
The diagram with the counterterm's interaction vertex placed as in Figure 3 cancels out the divergence from the loop in Figure 2.
图3所示的反项的交互顶点{{math|''Z''<sub>1</sub>}}的图抵消了图2中环的发散。
Historically, the splitting of the "bare terms" into the original terms and counterterms came before the renormalization group insight due to Kenneth Wilson. According to such renormalization group insights, detailed in the next section, this splitting is unnatural and actually unphysical, as all scales of the problem enter in continuous systematic ways.
Historically, the splitting of the "bare terms" into the original terms and counterterms came before the renormalization group insight due to Kenneth Wilson. According to such renormalization group insights, detailed in the next section, this splitting is unnatural and actually unphysical, as all scales of the problem enter in continuous systematic ways.
从历史上看，将“裸项”分解为原始项（？）和反项（？）的做法，早于肯尼思 · 威尔逊对重整化群的洞察。根据这些重整化群的洞察，在更细节的部分里这种分裂是非自然的也是非物理的，因为问题的所有尺度都是以连续的系统方式进入的（？）。
To minimize the contribution of loop diagrams to a given calculation (and therefore make it easier to extract results), one chooses a renormalization point close to the energies and momenta exchanged in the interaction. However, the renormalization point is not itself a physical quantity: the physical predictions of the theory, calculated to all orders, should in principle be independent of the choice of renormalization point, as long as it is within the domain of application of the theory. Changes in renormalization scale will simply affect how much of a result comes from Feynman diagrams without loops, and how much comes from the remaining finite parts of loop diagrams. One can exploit this fact to calculate the effective variation of physical constants with changes in scale. This variation is encoded by beta-functions, and the general theory of this kind of scale-dependence is known as the renormalization group.
To minimize the contribution of loop diagrams to a given calculation (and therefore make it easier to extract results), one chooses a renormalization point close to the energies and momenta exchanged in the interaction. However, the renormalization point is not itself a physical quantity: the physical predictions of the theory, calculated to all orders, should in principle be independent of the choice of renormalization point, as long as it is within the domain of application of the theory. Changes in renormalization scale will simply affect how much of a result comes from Feynman diagrams without loops, and how much comes from the remaining finite parts of loop diagrams. One can exploit this fact to calculate the effective variation of physical constants with changes in scale. This variation is encoded by beta-functions, and the general theory of this kind of scale-dependence is known as the renormalization group.
为了尽量减少环路图对给定计算的影响(从而使得计算结果更容易提取) ，可以选择一个接近相互作用中交换的能量和动量的重整化点。然而，重整化点本身并不是一个物理量: 在计算到所有的阶（？）之下，理论物理的预测，原则上应该独立于重整化点的选择，只要它在理论的应用范围内。重整化尺度的变化将影响无环费曼图产生的结果多少，以及来自环图剩余的有限部分的结果的多少。人们可以利用这一事实来计算物理常数随规模变化的有效变化。这种变化由 β 函数编码，这种尺度依赖的一般理论被称为重整化群。（OK）
Colloquially, particle physicists often speak of certain physical "constants" as varying with the energy of interaction, though in fact, it is the renormalization scale that is the independent quantity. This running does, however, provide a convenient means of describing changes in the behavior of a field theory under changes in the energies involved in an interaction. For example, since the coupling in quantum chromodynamics becomes small at large energy scales, the theory behaves more like a free theory as the energy exchanged in an interaction becomes large – a phenomenon known as asymptotic freedom. Choosing an increasing energy scale and using the renormalization group makes this clear from simple Feynman diagrams; were this not done, the prediction would be the same, but would arise from complicated high-order cancellations.
Colloquially, particle physicists often speak of certain physical "constants" as varying with the energy of interaction, though in fact, it is the renormalization scale that is the independent quantity. This running does, however, provide a convenient means of describing changes in the behavior of a field theory under changes in the energies involved in an interaction. For example, since the coupling in quantum chromodynamics becomes small at large energy scales, the theory behaves more like a free theory as the energy exchanged in an interaction becomes large – a phenomenon known as asymptotic freedom. Choosing an increasing energy scale and using the renormalization group makes this clear from simple Feynman diagrams; were this not done, the prediction would be the same, but would arise from complicated high-order cancellations.
通俗地说，粒子物理学家经常说的某些物理“常数”随着相互作用的能量而变化，尽管事实上，重整化标度才是独立量。然而，这种运行（？）确实提供了一种方便的手段来描述场理论在相互作用所涉及的能量变化下的行为变化。例如，由于量子色动力学中的耦合在大能量尺度下变小，该理论表现得更像一个自由理论（？），因为在相互作用中交换的能量变大了---- 这种现象被称为渐近自由（？）。选择一个递增的能量尺度并使用重整化群，可以从简单的费曼图中清楚地看出这一点; 如果不这样做，预测结果将是一样的，但是会出现复杂的高阶抵消。
<math>I=\int_0^a \frac{1}{z}\,dz-\int_0^b \frac{1}{z}\,dz=\ln a-\ln b-\ln 0 +\ln 0</math>
<math>I=\int_0^a \frac{1}{z}\,dz-\int_0^b \frac{1}{z}\,dz=\ln a-\ln b-\ln 0 +\ln 0</math>
< math > i = int _ 0 ^ a frac {1}{ z } ，dz-int _ 0 ^ b frac {1}{ z } ，dz = ln a-ln b-ln 0 + ln 0 </math >
<math>I=\int_0^a \frac{1}{z}\,dz-\int_0^b \frac{1}{z}\,dz=\ln a-\ln b-\ln 0 +\ln 0</math>
To eliminate the divergence, simply change lower limit of integral into and :
To eliminate the divergence, simply change lower limit of integral into and :
为了去除发散，只需将积分的下限改为{{mvar|ε<sub>a</sub>}}和{{mvar|ε<sub>b</sub>}}:
<math>I=\ln a-\ln b-\ln{\varepsilon_a}+\ln{\varepsilon_b} = \ln \tfrac{a}{b} - \ln \tfrac{\varepsilon_a}{\varepsilon_b}</math>
<math>I=\ln a-\ln b-\ln{\varepsilon_a}+\ln{\varepsilon_b} = \ln \tfrac{a}{b} - \ln \tfrac{\varepsilon_a}{\varepsilon_b}</math>
<math>I=\ln a-\ln b-\ln{\varepsilon_a}+\ln{\varepsilon_b} = \ln \tfrac{a}{b} - \ln \tfrac{\varepsilon_a}{\varepsilon_b}</math>
Making sure → 1}}, then ln .}}
Making sure → 1}}, then ln .}}
确保{{math|{{sfrac|''ε<sub>b</sub>''|''ε<sub>a</sub>''}} → 1}} ，然后 {{math|''I'' {{=}} ln {{sfrac|''a''|''b''}}.}}