sage
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Effective field theory.
There too many other stuff in the original post. I open this new thread to discuss walk_f's problems with renormalization.
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我并不是否认有效理论下对重整化不那么必要的讨论。
On the contrary, renormalization is absolutely necessary in an effective field theory. (see below)
只是有效理论让人感觉不太舒服:)
if it is only psychological...
（hehe 这个话可能要被很多人狠批 但是 对QCD这样的理论感觉到现在为止 我们的确还没找到一个比较好的有效理论，手征微扰论很漂亮(零阶时候) 但是适用的能区实在太小
能描述的物理粒子也太少太少。有效理论很强大 但不是我们的目标）
Then what is your goal? Effective theory is by definition only applicable in a range of scales. This is the best we have so far. Every field theory we use to describe nature these days are effective theories. They are not in principle different from chiral perturbation theory. Below the the scale of chiral symmetry breaking, chiral perturbation theory is a beautiful effective field theory. It is the only method we have to gain analytical control of physics at those scales.
个人感觉：可重整性并不是仅仅说：有一个紫外的物理的cutoff，在一定误差内，
理论就自洽了。它意味着的重正化不变. 1： 重整化不仅仅是处理紫外发散的。重整化不变性 有 或者没有 是物理的结论.
重整化不变性 意味着我们不仅能由低能标的Green函数出发得到的高能标下
的Green函数 也能反过来。
它本身包含的物理意思 感觉跟发散没关系。即使没发散，
具有这种不变性的话 就可以做重整化。
This is exactly the statement from an effective field theory point of view. Again, let me repeat. The theory is defined at some high energy scale with couplings (or not so correctly, 'bare' couplings). However, we want to deal have a theory which effectively and conveniently describes the low energy experiment. Therefore, we integrate out high momentum scales. This process changes (or renormalizes) the couplings away from their bare values.
This is what happens when we do renormalization.
At the same time, I could also in principle do the calculation with bare couplings. The result should be the same as using the renormalized couplings at a lower scale. This is exactly the statement of renormalization invariance that leads to Callan-Symanzik equations.
－在维数正规化里面 好像没看到需要紫外的cutoff
This is not true, Dimensional regularization is exactly a regulator which regulates the untra-violet divergenece. (See Georgi's review http://schwinger.harvard.edu/%7Egeorgi/index.htm)
2： 红外发散跟紫外发散具有类似的问题
重整化不变性意味着我们可以把微扰论中遇到的 所有紫外发散仍到 几个常数里面去。
个人感觉：
对QCD而言 夸克层次上振幅里面的红外发散(抵消不了的，并且在高能标时候 由于渐近 自由 这个振幅具有物理意义) 类似于重正化(实际上 我是看不出物理思想跟重整化有什么本质区别) 我们期望物理的夸克束缚态的描述能统一的吸收掉所有这些红外发散
(这个"能统一吸收"也肯定由某种不变性保证的 )－－－在这个做法里面
看不出涉及有效理论自然提供的cutoff所起到的作用......
It is technically similar but in principle different. the IR divergence is the effect of defining a asymptotic states in a IR non-trivial theory (either QCD or QED). The physical amplitude is indeed depends on the IR cutoff (in the easier to understand case of QED, it is determined by experimentally how well we can resolve a low energy photon away from an electron. In QCD, this has something to do with dressing up partons with gluons).
Ultraviolet cutoff of effective field theory of course does not say anything about its IR divergence. It should not.
The statement of effective field is that such a theory captures the essence of low energy physics after integrating out high energy physics.
| 发表时间：2005-04-16, 15:18:24 |
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walk_f