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The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry.

The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry.

*In mathematics, scale invariance usually refers to an invariance of individual [[function (mathematics)|functions]] or [[curve]]s. A closely related concept is [[self-similarity]], where a function or curve is invariant under a discrete subset of the dilations. It is also possible for the [[probability distribution]]s of [[random process]]es to display this kind of scale invariance or self-similarity.

*In mathematics, scale invariance usually refers to an invariance of individual [[function (mathematics)|functions]] or [[curve]]s. A closely related concept is [[self-similarity]], where a function or curve is invariant under a discrete subset of the dilations. It is also possible for the [[probability distribution]]s of [[random process]]es to display this kind of scale invariance or self-similarity.

*In general, dimensionless quantities are scale invariant. The analogous concept in statistics are standardized moments, which are scale invariant statistics of a variable, while the unstandardized moments are not.

*In general, dimensionless quantities are scale invariant. The analogous concept in statistics are standardized moments, which are scale invariant statistics of a variable, while the unstandardized moments are not.

 

* 在数学中，标度不变性通常指单个函数或曲线的不变性。与此密切相关的概念是'''Self-similarity 自相似性'''，其中函数或曲线在膨胀的离散子集下是不变的。随机过程的概率分布也可能表现出这种标度不变性或自相似性。

* 在数学中，尺度不变性通常指单个函数或曲线的不变性。一个密切相关的概念是自相似性，其中一个函数或曲线在膨胀的一个离散子集下是不变的。随机过程的概率分布也可能表现出这种尺度不变性或自相似性。

* 在经典场论中，尺度不变性最常用于整个理论在扩张下的不变性。这些理论典型地描述了没有特征长度尺度的经典物理过程。

* 在经典场论中，尺度不变性最常用于整个理论在扩张下的不变性。这些理论典型地描述了没有特征长度尺度的经典物理过程。

* 在量子场论中，尺度不变性对粒子物理学有一种解释。在尺度不变理论中，粒子相互作用的强度并不依赖于所涉及的粒子的能量。

* 在量子场论中，尺度不变性对粒子物理学有一种解释。在尺度不变理论中，粒子相互作用的强度并不依赖于所涉及的粒子的能量。