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For example, an electron theory may begin by postulating an electron with an initial mass and charge. In quantum field theory a cloud of virtual particles, such as photons, positrons, and others surrounds and interacts with the initial electron. Accounting for the interactions of the surrounding particles (e.g. collisions at different energies) shows that the electron-system behaves as if it had a different mass and charge than initially postulated. Renormalization, in this example, mathematically replaces the initially postulated mass and charge of an electron with the experimentally observed mass and charge. Mathematics and experiments prove that positrons and more massive particles like protons, exhibit precisely the same observed charge as the electron - even in the presence of much stronger interactions and more intense clouds of virtual particles.

For example, an electron theory may begin by postulating an electron with an initial mass and charge. In quantum field theory a cloud of virtual particles, such as photons, positrons, and others surrounds and interacts with the initial electron. Accounting for the interactions of the surrounding particles (e.g. collisions at different energies) shows that the electron-system behaves as if it had a different mass and charge than initially postulated. Renormalization, in this example, mathematically replaces the initially postulated mass and charge of an electron with the experimentally observed mass and charge. Mathematics and experiments prove that positrons and more massive particles like protons, exhibit precisely the same observed charge as the electron - even in the presence of much stronger interactions and more intense clouds of virtual particles.

例如，一个电子理论会先假定电子具有初始质量和电荷。在量子场论中，一个由诸如光子、正电子等虚粒子组成的云团围绕着初始电子并与之相互作用。考虑到周围粒子的相互作用(例如: 不同能量的碰撞)表明电子-系统的行为宛如它有不同于最初假设的质量和电荷。重整化，在这个例子中，在数学上用实验观察到的质量和电荷代替了最初假设的电子的质量和电荷。数学和实验证明，正电子和质子等质量更大的粒子，即使存在更强烈的相互作用和更密集的虚粒子云，其电荷也与电子完全相同。（暂未高光专有名词）

例如，一个电子理论会先假定电子具有初始质量和电荷。在量子场论中，一个由诸如光子、正电子等虚粒子组成的云团围绕着初始电子并与之相互作用。考虑到周围粒子的相互作用(例如: 不同能量的碰撞)表明电子-系统的行为宛如它有不同于最初假设的质量和电荷。重整化，在这个例子中，在数学上用实验观察到的质量和电荷代替了最初假设的电子的质量和电荷。数学和实验证明，正电子和质子等质量更大的粒子，即使存在更强烈的相互作用和更密集的虚粒子云，其电荷也与电子完全相同。

Renormalization specifies relationships between parameters in the theory when parameters describing large distance scales differ from parameters describing small distance scales. In high-energy particle accelerators like the CERN Large Hadron Collider the concept named pileup occurs when undesirable proton-proton collisions interact with data collection for simultaneous, nearby desirable measurements. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in further infinities. When describing space-time as a continuum, certain statistical and quantum mechanical constructions are not well-defined. To define them, or make them unambiguous, a continuum limit must carefully remove "construction scaffolding" of lattices at various scales. Renormalization procedures are based on the requirement that certain physical quantities (such as the mass and charge of an electron) equal observed (experimental) values. That is, the experimental value of the physical quantity yields practical applications, but due to their empirical nature the observed measurement represents areas of quantum field theory that require deeper derivation from theoretical bases.

Renormalization specifies relationships between parameters in the theory when parameters describing large distance scales differ from parameters describing small distance scales. In high-energy particle accelerators like the CERN Large Hadron Collider the concept named pileup occurs when undesirable proton-proton collisions interact with data collection for simultaneous, nearby desirable measurements. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in further infinities. When describing space-time as a continuum, certain statistical and quantum mechanical constructions are not well-defined. To define them, or make them unambiguous, a continuum limit must carefully remove "construction scaffolding" of lattices at various scales. Renormalization procedures are based on the requirement that certain physical quantities (such as the mass and charge of an electron) equal observed (experimental) values. That is, the experimental value of the physical quantity yields practical applications, but due to their empirical nature the observed measurement represents areas of quantum field theory that require deeper derivation from theoretical bases.

当描述大距离尺度的参数不同于描述小距离尺度的参数时，重整化指定了理论中参数之间的关系。在像欧洲核子研究中心这样的高能粒子加速器中，当质子-质子的不和需求的碰撞与同时临近的可取测量数据相互作用时，就会产生连环相撞（？pileup）的概念。从物理上来说，涉及某一问题的无限量级在累积后可能会导致进一步的无限量。当把时空描述为一个连续统时，某些统计的和量子力学的结构没有得到很好的定义。为了定义它们，或者使它们毫不含糊，连续统的限制必须能够小心地移除不同尺度的晶格的“结构脚手架（？）”。重整化过程的基础要求某些物理量(如电子的质量和电荷)等于观察到的(实验)值。也就是说，物理量的实验值虽能产生实际应用，但由于它们的经验性本质，所观察到的测量代表了量子场论中那些需要从理论基础进行更深入的推导的领域。（暂未高光专有名词）

当描述大距离尺度的参数不同于描述小距离尺度的参数时，重整化指定了理论中参数之间的关系。在像欧洲核子研究中心这样的高能粒子加速器中，当质子-质子的不和需求的碰撞与同时临近的可取测量数据相互作用时，就会产生连环相撞（？pileup）的概念。从物理上来说，涉及某一问题的无限量级在累积后可能会导致进一步的无限量。当把时空描述为一个连续统时，某些统计的和量子力学的结构没有得到很好的定义。为了定义它们，或者使它们毫不含糊，连续统的限制必须能够小心地移除不同尺度的晶格的“结构脚手架（？）”。重整化过程的基础要求某些物理量(如电子的质量和电荷)等于观察到的(实验)值。也就是说，物理量的实验值虽能产生实际应用，但由于它们的经验性本质，所观察到的测量代表了量子场论中那些需要从理论基础进行更深入的推导的领域。

Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics.

Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics.

Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Nikolay Bogolyubov and Kenneth Wilson, the focus is on variation of physical quantities across contiguous scales, while distant scales are related to each other through "effective" descriptions. All scales are linked in a broadly systematic way, and the actual physics pertinent to each is extracted with the suitable specific computational techniques appropriate for each. Wilson clarified which variables of a system are crucial and which are redundant.

Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Nikolay Bogolyubov and Kenneth Wilson, the focus is on variation of physical quantities across contiguous scales, while distant scales are related to each other through "effective" descriptions. All scales are linked in a broadly systematic way, and the actual physics pertinent to each is extracted with the suitable specific computational techniques appropriate for each. Wilson clarified which variables of a system are crucial and which are redundant.

今天，观点发生了转变: 基于重整化群尼古拉·博戈柳博夫和 Kenneth Wilson 的突破性见解，重点在于连续尺度间物理量的变化，而远距离尺度通过有效的描述彼此相关。所有尺度都以广泛系统的方式联系在一起，与每个尺度相关的实际物理学用适合每个尺度的特定计算技术提取出来。威尔逊澄清了系统中哪些变量是至关重要的，哪些是冗余的。

今天，观点发生了转变: 基于尼古拉·博戈柳博夫和 Kenneth Wilson 对重整化群的突破性见解，关注点成为连续尺度间物理量的变化，而相隔较远的尺度通过“有效的“（？）描述彼此相关。广泛来说，所有尺度都以系统的方式联系在一起。同时，与每个尺度相关的实际物理学被适合于每个尺度的特定计算技术提取出来。威尔逊阐明了系统中哪些变量是至关重要的，而哪些又是冗余的。

Renormalization is distinct from regularization, another technique to control infinities by assuming the existence of new unknown physics at new scales.

Renormalization is distinct from regularization, another technique to control infinities by assuming the existence of new unknown physics at new scales.