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Renormalization of QED
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sage 发表文章数: 1125 |
Renormalization of QED 为了避免无用功,先统一一下名词术语。 我所理解的基本概念是(以QED为例,在单圈图水平上): 1)电子自能过程。由电子内线和光子内线构成的封闭圈图,属于电子自能过程。内线也即你所说的传播子。即电子放出一个虚光子随机又吸收这个虚光子的过程。 2)真空极化过程。由一对正反电子内线构成的封闭圈描写,属于光子变为一对虚正反粒子对随即这对虚正反粒子又湮灭成光子的过程。 3)顶角修正。这个不好用文字说明,这里我们应该不会有术语分歧。 我所了解的lamb shift ,在单圈图近似下,同时包含了以上三种基本过程的辐射修正,同时涉及几个重整化量,而不仅仅是真空极化。 The most general vertex function of electron couples to photon is Gamma^mu F_1(q^2)+ (i \sigma*q /2m)*F_2(q^2) F_1 and F_2 are form factors. In calculating Lambs shift, the second term is irrelavent since it is the magnetic dipole interaction. In hydrogen atom, the relavent wavelength is much longer than electron mass. Therefore, we could choose q->0. The semi-classical potential interaction is then from Gamma_mu F_1(0)*(photon propagator). There are electron self-energy and vertex corrections to F_1(0). However, they exactly CANCEL each other as required by the Ward Identity (or equivalently, gauge symmetry). The only possible correction is from the wave-function renormalization of the PHOTON propagator, i.e., vacuum polarization. 关于真空涨落。首先经典地看,假定真空一无所有,没有任何场量(物质),没有任何能量。然后,考虑量子力学效应(最初级贡献与广义正则共轭对不对易有关,注意到产生算子和湮灭算子之间的对易子源于正则共轭对之间的对易关系,而通常所说的零点能直接由产生算子和湮灭算子之间的对易子而来)。即从初级贡献看,由于不确定关系,真空不是对应“零”,而是“正”和“负”之间“来回振荡”,其平均值为零,但方差均值并不为零,通常所说的零点能可看作这种现象下的一个特例。 作为一个例子,考虑电磁场真空,这样的真空中,电磁场场强的平均值为零,但瞬时值并不为零,而是上下波动,上下涨落,因此它的平方的平均值并不为零。电磁场的能量与场强的平方成正比,因此电磁场的真空涨落将贡献一个电磁场真空的零点能——这是可以严格定量计算得出的结论。通常的教科书里面,只是通常场的量子化给出零点能的物理概念,却没有进一步深究其物理含义。 Very good. Unfortunately, Lamb's shift is not proportional field strength square. Therefore, they are not zero point fluctuation even by your standard. Your definition would mean the vacuum energy is something like <0|F_munu F^munu |0>. Unfortunately, the zero point energy does not come from this operator. It is proportional to <0|0>
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星空浩淼 发表文章数: 1743 |
Re: Renormalization of QED 对Lambs shift的定性解释,可见: T.A.Welton, Phys.Rev.74,1157(1948) BTW,文献里常有利用真空态下电磁场场强平方对空间积分等于电磁场零点能之和的公式。 关于Lambs shift的具体来源,sage兄多半是对的。我记得在对电子磁矩的修正和Lambs shift所对应的修正两样合在一起的公式里面,同时对应三种基本发散圈图的修正,其中代表Lambs shift的项里,同时包含重整化的电荷和重整化的质量等等。由于三种基本圈图贡献不同的重整化常数,所以我判断Lambs shift同时包含三种基本圈图的辐射修正贡献。 唯有与时间赛跑,方可维持一息尚存
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sage 发表文章数: 1125 |
Re: Renormalization of QED I just realized that I might have created some confusion about Lamb shift. I was thinking that Ping2 Zong1 is talking about the part in Lamb's shift which might remotely resemble zero point energy. that is the modification of Coulomb potential part purly due to vacuum polarization, due to Ward indentity. However, the complete Lamb's shift surely have contributions from vertex corrections and magnetic interections. However, they do not in anyway resemble vacuum oscillation.
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