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第334行： − A simple example of a scale-invariant QFT is the quantized electromagnetic field without charged particles. This theory actually has no coupling parameters (since photons are massless and non-interacting) and is therefore scale-invariant, much like the classical theory.+ − − 标度不变量 QFT 的一个简单例子是没有带电粒子的量子化电磁场。这个理论实际上没有耦合参数(因为光子是无质量和非相互作用的) ，因此是尺度不变的，很像经典理论。 − However, in nature the electromagnetic field is coupled to charged particles, such as electrons. The QFT describing the interactions of photons and charged particles is quantum electrodynamics (QED), and this theory is not scale-invariant. We can see this from the QED beta-function. This tells us that the electric charge (which is the coupling parameter in the theory) increases with increasing energy. Therefore, while the quantized electromagnetic field without charged particles is scale-invariant, QED is not scale-invariant.+ − − 然而，在自然界中，电磁场是与带电粒子耦合的，比如电子。描述光子和带电粒子相互作用的量子力学理论是量子电动力学的，而且这个理论不是标度不变的。我们可以从 QED beta 函数中看到这一点。这告诉我们电荷(在理论上是耦合参数)随着能量的增加而增加。因此，尽管没有带电粒子的量子化电磁场是尺度不变的，QED 却不是尺度不变的。
→Quantum electrodynamics 量子电动力学
A simple example of a scale-invariant QFT is the quantized electromagnetic field without charged particles. This theory actually has no coupling parameters (since [[photon]]s are massless and non-interacting) and is therefore scale-invariant, much like the classical theory.
A simple example of a scale-invariant QFT is the quantized electromagnetic field without charged particles. This theory actually has no coupling parameters (since [[photon]]s are massless and non-interacting) and is therefore scale-invariant, much like the classical theory.
标度不变量子场论的一个简单实例是没有带电粒子的量子化电磁场。这个理论实际上没有耦合参数(因为光子是无质量和非相互作用的) ，因此是标度不变的，这很像经典理论。
However, in nature the electromagnetic field is coupled to charged particles, such as [[electron]]s. The QFT describing the interactions of photons and charged particles is [[quantum electrodynamics]] (QED), and this theory is not scale-invariant. We can see this from the [[beta-function#Quantum electrodynamics|QED beta-function]]. This tells us that the [[electric charge]] (which is the coupling parameter in the theory) increases with increasing energy. Therefore, while the quantized electromagnetic field without charged particles '''is''' scale-invariant, QED is '''not''' scale-invariant.
However, in nature the electromagnetic field is coupled to charged particles, such as [[electron]]s. The QFT describing the interactions of photons and charged particles is [[quantum electrodynamics]] (QED), and this theory is not scale-invariant. We can see this from the [[beta-function#Quantum electrodynamics|QED beta-function]]. This tells us that the [[electric charge]] (which is the coupling parameter in the theory) increases with increasing energy. Therefore, while the quantized electromagnetic field without charged particles '''is''' scale-invariant, QED is '''not''' scale-invariant.
然而在自然界中，电磁场是与带电粒子耦合的，比如电子。描述光子和带电粒子相互作用的量子场论是量子电动力学，而这个理论并不是标度不变的。我们可以从量子电动力学的β函数中得到这一认识。这就告诉我们电荷(在理论上是耦合参数)随着能量的增加而增加。因此，尽管没有带电粒子的量子化电磁场是标度不变的，量子电动力学却不是标度不变的。
===Massless scalar field theory 无质量标量场理论===
===Massless scalar field theory 无质量标量场理论===