更改

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<!--boldface per WP:R#PLA; 'Self-interaction' and 'Self-interactions' redirect here-->. 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.

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<!--boldface per WP:R#PLA; 'Self-interaction' and 'Self-interactions' redirect here-->. 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.

'''<font color="#ff8000"> 重整化 Renormalization </font>'''是'''<font color="#ff8000"> 量子场论 Quantum Field Theory </font>'''、场的'''<font color="#ff8000"> 统计力学 Statistical Mechanics </font>'''和'''<font color="#32cd32"> 自相似 Self-similarity </font>'''几何结构理论中,通过改变计算量的值以抵消其'''<font color="#32cd32"> 自相互作用 Self-interaction </font>'''，进而消除计算量中产生的'''<font color="#ff8000"> 无穷大 infinities </font>'''的一系列技巧集合。但是，即使在量子场论'''<font color="#ff8000"> </font>'''的'''<font color="#32d32"> 环路图 loop diagrams </font>'''中没有无穷数，对原'''<font color="#32d32"> 拉格朗日场理论 Lagrangian (Field Theory) </font>'''中出现的质量和场进行重整化的必要性也可以得到证明。

'''<font color="#ff8000">重整化 Renormalization </font>'''是应用于 '''<font color="#ff8000">量子场论 Quantum Field Theory </font>'''、场的'''<font color="#ff8000">统计力学 Statistical Mechanics </font>'''和'''<font color="#32cd32">自相似 Self-similar</font>'''几何结构理论中的一类方法。通过重整化，可以改变计算量的值以抵消其'''<font color="#32cd32"> 自相互作用 Self-interaction </font>'''，进而消除计算量中产生的'''<font color="#ff8000"> 无穷大 infinities</font>'''。但是，即使在量子场论的'''<font color="#32d32"> 圈图 loop diagrams </font>'''中没有出现无穷大，对原'''<font color="#32d32"> 拉格朗日场理论 Lagrangian (Field Theory) </font>'''中出现的质量和场进行重整化也是必要的。

 

 

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 particle]]s, such as [[photon]]s, [[positron]]s, 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 [[proton]]s, 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 particle]]s, such as [[photon]]s, [[positron]]s, 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 [[proton]]s, 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.

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'''<font color="#ff8000"> 电子 Electron </font>'''理论会先假定电子具有初始质量和电荷。在'''<font color="#ff8000"> 量子场论 </font>'''中，一个由诸如'''<font color="#ff8000"> 光子 Photon </font>'''、'''<font color="#ff8000"> 正电子 Positron </font>'''等'''<font color="#ff8000"> 虚粒子 Virtual Particle </font>'''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'''<font color="#ff8000"> 质子 Proton </font>'''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。

例如，'''<font color="#ff8000"> 电子 Electron </font>'''理论会先假定电子具有初始质量和电荷。在'''<font color="#ff8000"> 量子场论 </font>'''中，一个由诸如'''<font color="#ff8000"> 光子 Photon</font>'''、'''<font color="#ff8000">正电子 Positron </font>'''等'''<font color="#ff8000"> 虚粒子 Virtual Particle </font>'''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。在这个例子中，重整化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质量和电荷。数学和实验证明，正电子和'''<font color="#ff8000"> 质子 Proton </font>'''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 [[Large Hadron Collider|CERN Large Hadron Collider]] the concept named [[Pileup (disambiguation)|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 [[Space-time continuum|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 [[Large Hadron Collider|CERN Large Hadron Collider]] the concept named [[Pileup (disambiguation)|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 [[Space-time continuum|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.

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'''<font color="#32cd32"> 连环相撞 Pileup </font>'''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'''<font color="#32cd32"> 时空连续统 Space-time Continuum</font>'''时，某些统计的和量子力学的结构没有得到'''<font color="#32cd32"> 明确定义 Well-defined </font>'''。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。

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的高能粒子加速器中，当不理想的质子-质子碰撞与同时临近的可取测量数据相互作用时，就会产生'''<font color="#32cd32"> 连环相撞 Pileup </font>'''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'''<font color="#32cd32"> 时空连续统 Space-time Continuum</font>'''时，某些统计的和量子力学的结构没有得到'''<font color="#32cd32"> 明确定义 Well-defined </font>'''。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。