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重整化 (查看源代码)

2021年8月20日 (五) 00:28的版本

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删去专有名词多余的英语表达

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Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian.

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''' 重整化 Renormalization '''是''' 量子场论 Quantum Field Theory '''、场的''' 统计力学 Statistical Mechanics '''和''' 自相似 Self-similarity '''几何结构理论中,通过改变计算量的值以抵消其''' 自相互作用 Self-interaction '''，进而消除计算量中产生的''' 无穷大 infinities '''~~的一系列技巧集合。但是，即使在~~''' ~~量子场论 Quantum Field Theory~~ '''的''' 环路图 loop diagrams '''中没有无穷数，对原''' 拉格朗日场理论 Lagrangian (Field Theory) '''中出现的质量和场进行重整化的必要性也可以得到证明。

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''' 重整化 Renormalization '''是''' 量子场论 Quantum Field Theory '''、场的''' 统计力学 Statistical Mechanics '''和''' 自相似 Self-similarity '''几何结构理论中,通过改变计算量的值以抵消其''' 自相互作用 Self-interaction '''，进而消除计算量中产生的''' 无穷大 infinities '''的一系列技巧集合。但是，即使在量子场论''' '''的''' 环路图 loop diagrams '''中没有无穷数，对原''' 拉格朗日场理论 Lagrangian (Field Theory) '''中出现的质量和场进行重整化的必要性也可以得到证明。

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== Self-interactions in classical physics ==

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[[Image:Renormalized-vertex.png|thumbnail|upright=1.3|Figure 1. Renormalization in quantum electrodynamics: The simple electron/photon interaction that determines the electron's charge at one renormalization point is revealed to consist of more complicated interactions at another.]]

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[[Image:Renormalized-vertex.png|thumbnail|upright=1.3|Figure 1. Renormalization in quantum electrodynamics: The simple electron/photon interaction that determines the electron's charge at one renormalization point is revealed to consist of more complicated interactions at another.|链接=Special:FilePath/Renormalized-vertex.png]]

Figure 1. Renormalization in quantum electrodynamics: The simple electron/photon interaction that determines the electron's charge at one renormalization point is revealed to consist of more complicated interactions at another.

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[[Image:vacuum polarization.svg|thumb|(a) Vacuum polarization, a.k.a. charge screening. This loop has a logarithmic ultraviolet divergence.]]

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[[Image:vacuum polarization.svg|thumb|(a) Vacuum polarization, a.k.a. charge screening. This loop has a logarithmic ultraviolet divergence.|链接=Special:FilePath/Vacuum_polarization.svg]]

(a) Vacuum polarization, a.k.a. charge screening. This loop has a logarithmic ultraviolet divergence.

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(a) Vacuum polarization, a.k.a.电荷屏蔽。这个环有一个对数的紫外辐散。

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[[Image:selfE.svg|thumb|(b) Self-energy diagram in QED]]

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[[Image:selfE.svg|thumb|(b) Self-energy diagram in QED|链接=Special:FilePath/SelfE.svg]]

(b) Self-energy diagram in QED

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(b)量子电动力学中的自能图

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[[Image:Penguin diagram.JPG|thumb|(c) Example of a “penguin” diagram]]

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[[Image:Penguin diagram.JPG|thumb|(c) Example of a “penguin” diagram|链接=Special:FilePath/Penguin_diagram.JPG]]

(c) Example of a “penguin” diagram

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=== A loop divergence ===

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[[Image:Loop-diagram.png|thumb|upright=1.1|Figure 2. A diagram contributing to electron–electron scattering in QED. The loop has an ultraviolet divergence.]]

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[[Image:Loop-diagram.png|thumb|upright=1.1|Figure 2. A diagram contributing to electron–electron scattering in QED. The loop has an ultraviolet divergence.|链接=Special:FilePath/Loop-diagram.png]]

Figure 2. A diagram contributing to electron–electron scattering in QED. The loop has an ultraviolet divergence.

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=== Renormalization in QED ===

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[[Image:Counterterm.png|thumb|upright=1.1|Figure 3. The vertex corresponding to the {{math|''Z''1}} counterterm cancels the divergence in Figure 2.]]

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[[Image:Counterterm.png|thumb|upright=1.1|Figure 3. The vertex corresponding to the {{math|''Z''1}} counterterm cancels the divergence in Figure 2.|链接=Special:FilePath/Counterterm.png]]

Figure 3. The vertex corresponding to the counterterm cancels the divergence in Figure 2.

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In QFT, the value of a physical constant, in general, depends on the scale that one chooses as the renormalization point, and it becomes very interesting to examine the renormalization group running of physical constants under changes in the energy scale. The coupling constants in the Standard Model of particle physics vary in different ways with increasing energy scale: the coupling of quantum chromodynamics and the weak isospin coupling of the electroweak force tend to decrease, and the weak hypercharge coupling of the electroweak force tends to increase. At the colossal energy scale of 1015 GeV (far beyond the reach of our current particle accelerators), they all become approximately the same size (Grotz and Klapdor 1990, p. 254), a major motivation for speculations about grand unified theory. Instead of being only a worrisome problem, renormalization has become an important theoretical tool for studying the behavior of field theories in different regimes.

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在 QFT 中，一个物理常数的值，一般来说，取决于我们选择的重整化点的尺度，在能量尺度变化的情况下，研究重整化群物理常数的运行变得非常有趣。粒子物理标准模型中的耦合常数随着能量的增加而以不同的方式变化: 量子色动力学的耦合和电弱力的弱同位旋耦合趋于减小，电弱力的弱超荷耦合趋于增加。在10 15 ~~~~ GeV 的巨大能量范围内(远远超出我们现有的粒子加速器的能量范围) ，它们都变得大致相同(Grotz 和 Klapdor 1990，p. 254) ，这是推测大统一理论的主要动机。重整化已经不再是一个令人担忧的问题，而是成为研究不同区域中场理论行为的一个重要理论工具。

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在 QFT 中，一个物理常数的值，一般来说，取决于我们选择的重整化点的尺度，在能量尺度变化的情况下，研究重整化群物理常数的运行变得非常有趣。粒子物理标准模型中的耦合常数随着能量的增加而以不同的方式变化: 量子色动力学的耦合和电弱力的弱同位旋耦合趋于减小，电弱力的弱超荷耦合趋于增加。在10 15 GeV 的巨大能量范围内(远远超出我们现有的粒子加速器的能量范围) ，它们都变得大致相同(Grotz 和 Klapdor 1990，p. 254) ，这是推测大统一理论的主要动机。重整化已经不再是一个令人担忧的问题，而是成为研究不同区域中场理论行为的一个重要理论工具。

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