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量子场论问题之三
1 为什么同位旋对称性只适用于上夸克与下夸克。这岂不是让三代很不相同？
2 怎么从量子场论中反映同位旋以及奇异数这些物理量？
Faith, Fashion and Fancy.
Welcome to 我的域名：http://hongbaozhang.blog.edu.cn
| 发表时间：2005-06-28, 00:13:34 |
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星空浩淼
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Re: 量子场论问题之三
粒子物理跟量子场论不同之处，在于前者多少有些象是查数据表:-)，许久不翻，就容易忘。
我说的可能不全准确：
同位旋、奇异数这些东西，是一些唯象的（phenomenological）概念，如果要在量子场论那里体现，依靠手加进去，而不是从第一原理出发得来的。
“同位旋”是一种类比的概念，跟粒子不同自旋状态构成的多重态进行类比，来引入一种“旋”数学形式地描述一些多重态。
在解释一些粒子反应为什么能发生和为什么不能发生时，经常引入一些唯象的量子数，如奇异数等，把量子数守恒来作为粒子反应遵循的禁戒条件。
唯有与时间赛跑，方可维持一息尚存
| 发表时间：2005-06-28, 00:51:02 |
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sage
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Re: 量子场论问题之三
1 为什么同位旋对称性只适用于上夸克与下夸克。这岂不是让三代很不相同？
If you are refering to weak isospin, it applies to all three generations.
If you are talking about flavor symmetry of QCD, it is naturally broken by the quark mass. even the SU(2) for the u and d quark is just an approximation. Such global symmetries are only useful because we know they are only broken slightly, by small quark masses. It is not very good for strange already, even worse for others.
2 怎么从量子场论中反映同位旋以及奇异数这些物理量？
the existence a good (or approximately good) quantum number means the existence of a symmetry (or an approximate symmetry). Therefore, it provides constriants on the possible lagrangian.
| 发表时间：2005-06-28, 08:51:22 |
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HPC
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Re: 量子场论问题之三
我指的是味对称性，这么说这种同位旋并不是QCD所有，而是QCD之外的内容？那么这些对称性岂不是很不漂亮，没有一个更深层次的解释。
Faith, Fashion and Fancy.
Welcome to 我的域名：http://hongbaozhang.blog.edu.cn
| 发表时间：2005-06-28, 11:07:40 |
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sage
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Re: 量子场论问题之三
我指的是味对称性，这么说这种同位旋并不是QCD所有，而是QCD之外的内容？那么这些对称性岂不是很不漂亮，没有一个更深层次的解释。
if quarks are massless, QCD has a flavor symmetry. In reality, some quarks have small masses and some large. Therefore, we can only talk approximate about flavor symmetry for the light quarks. there could be a deeper understanding of flavor, we just do not know it yet.
By the way, a symmetry is broken does not mean it is useless. In the case of QCD, for the light quarks, chiral perturbation theory with approximate flavor symmetries is still very powerful.
most of the symmetries in nature are broken. That does not mean they are useless. On the ocntrary, they are very powerful.
| 发表时间：2005-06-28, 11:17:40 |
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HPC
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Re: 量子场论问题之三
我不是很清楚零质量和味对称性有什么直接的关联, 如果夸克的质量相等尽管不为零，是否也有味对称性。此外这味对称性指的只是同代夸克之间的对称性吧？也就是SU(2)不是SU(6)吧？
Faith, Fashion and Fancy.
Welcome to 我的域名：http://hongbaozhang.blog.edu.cn
| 发表时间：2005-06-28, 12:51:44 |
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sage
发表文章数: 1125
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Re: 量子场论问题之三
我不是很清楚零质量和味对称性有什么直接的关联, 如果夸克的质量相等尽管不为零，是否也有味对称性。此外这味对称性指的只是同代夸克之间的对称性吧？也就是SU(2)不是SU(6)吧？
in order to make our life easier, let's consider a model with two flavors, say u and d. this simple setup is enough to understand the effect of mass.
so the degrees of freedom we have is u_L, d_L, u_R and d_R, where L,R are chirality indices.
now write down the QCD lagrangian. an inspection of that Lagrangian shows there are the following globle symmetries
U(2)_L under which u_L and d_L forms a doublet
U(2)_R under which u_R and d_R forms a doublet
therefore, there is total U(2)_L\times U(2)_R global symmetries. From here, we can do two things.
1) if we turn on equal mass terms for u and d as you said, the mass terms will be
m(u_L u_R + d_L d_R)
this mass term (although equal for u and d), breaks the global symmetry down to its diagonal subgroup
U(2)_L \times U(2)_R ---> U(2)_D
where the generators of U(2)_D t_D=t_L + t_R.
2) In realistic QCD, we have first QCD phase transition through the formation of condensate
<u_L u_R+d_L d_R> \neq 0
this also breaks the global symmetries to its diagonal U(2)_D. Since this the spontaneous breaking, there are Goldstones (4 corrsponds to broken U(2)).
Then, there are quark masses. m_u and m_d (not equal). This explicitly break all the remaining global symmetry. Therefore, the goldstones all get mass. but because the breaking is small, the goldstones are all light. Indeed, we see three light mesons, they are pions..
we are still missing one goldstone. this is because the global symmetry we have above are only classical symmetries. quantum anomaly (chiral anomally) remove one of them. therefore, we do not have the fourth goldstone.
this is the simplest demonstration of the power of chiral perturbation theory.
| 发表时间：2005-06-28, 14:38:30 |
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