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如何估计弱电破缺的能标
planck能标是通过G,c,h构造出来的.似乎很直观.
那么大统一能标和弱电破缺的能标是怎么估计出来的???
手征相变的能标呢?
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| 发表时间：2005-11-17, 23:11:16 |
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kanex
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Re: 如何估计弱电破缺的能标
running coupling.
江畔何人初见月`江月何年初照人`
| 发表时间：2005-11-17, 23:26:40 |
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sage
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Re: 如何估计弱电破缺的能标
planck能标是通过G,c,h构造出来的.似乎很直观.
那么大统一能标和弱电破缺的能标是怎么估计出来的???
手征相变的能标呢?
Planck scale is obtained not by construction.. it is obtained by measuring gravity. It is obvious in the correct unit system in which h=c=1
Planck scale is obtained from the fact that G_N, the coupling constant, is dimensionful. Its value is just M_P^-2.
For the weak interaction, we have exactly the same thing in Fermi theory in which Fermi constant is dimensionful, its value is (with some 4pi around ) M_W^-2, W boson mass.
Chiral symmetry is already violated by weak interaction itself.
On the other hand, I am assuming you are talking about chiral symmetry breaking in QCD. It happened, well, at QCD scale, which is around the proton mass. It could again be measured as some dimensionful coupling in the meson-baryon effective theory.
| 发表时间：2005-11-18, 08:50:46 |
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轩轩
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Re: 如何估计弱电破缺的能标
thanks sage
For the weak interaction, we have exactly the same thing in Fermi theory in which Fermi constant is dimensionful, its value is (with some 4pi around ) M_W^-2, W boson mass.
su(2)李代数的耦合常数是这个M_W吗???
这些能标全是measure出来的?
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i will love you till the null infinity.
| 发表时间：2005-11-21, 18:43:06 |
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卢昌海
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Re: 如何估计弱电破缺的能标
:: su(2)李代数的耦合常数是这个M_W吗???
SU(2) coupling in electroweak theory is dimensionless, m_w^{-2} is the coupling in the effective langrangian for current interactions (four fermion interactions).
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| 发表时间：2005-11-21, 19:06:47 |
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轩轩
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Re: 如何估计弱电破缺的能标
thanks changhai
current interactions 是不是与所谓的流代数有关系??? 流代数与virasoro代数是什么关系?:)
witten有300多篇文章,评价他我用2个字:大文豪.
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| 发表时间：2005-11-21, 19:13:54 |
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sage
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Re: 如何估计弱电破缺的能标
The moral of the story is: at energy scales much lower than the mass of the W boson, we should be able to integrate out the W boson. The resulting effective Lagrangian contain four fermion interactions of the form
(1/M_W^2) (4 fermion operator).
This Lagrangian actually known long before we know there is a W boson. This is called fermi theory of weak interactions. M_W^2 is the scale of the weak interaction, i.e., the scale at which this four fermion Lagrangian should be replaced by a renormalizable one.
The four fermion operators could be written as
j_mu j^mu
where j_mu is the weak current made of fermion bilinears.
current interactions 是不是与所谓的流代数有关系???
current algebra is the commutation relation between currents.
流代数与virasoro代数是什么关系?:)
sure. virasoro algebra is the current algebra between energy momentum tensor of 2d conformal field theory.
| 发表时间：2005-11-21, 22:00:51 |
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轩轩
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Re: 如何估计弱电破缺的能标
thanks sage :)
是否所有共形场论全描写无质量场???
twistor理论似乎全处理无质量场,它似乎与CFT有很大的关系.?
witten有300多篇文章,评价他我用2个字:大文豪.
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i will love you till the null infinity.
| 发表时间：2005-11-22, 00:18:41 |
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轩轩
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Re: 如何估计弱电破缺的能标
还有一个问题
noether定理告诉我们,一个等度量变换导致一个守恒量.共形对称性导致什么守恒的量??存在吗??
witten有300多篇文章,评价他我用2个字:大文豪.
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i will love you till the null infinity.
| 发表时间：2005-11-22, 00:42:24 |
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sage
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Re: 如何估计弱电破缺的能标
是否所有共形场论全描写无质量场???
classically, or in a free theory, yes. since classically, mass term is not dimensionless, therefore, a massive theory is not conformally invariant. On the other hand, in theory with interactions, especially when the interaction is strong, this conclusion is no longer valid. In that case, the quantum correction to the scaling dimension of the mass term, called anomalous dimension, is large. In that case, there could be points where a Lagrangian with a non-zero bare mass term could be conformal. Sometimes, this goes by the name of wilson-fisher fix point.
twistor理论似乎全处理无质量场,它似乎与CFT有很大的关系.?
Of course it is. as far as i can tell, twistor has some success in the theories with a lot of supersymmetries and conformal.
| 发表时间：2005-11-22, 09:10:42 |
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sage
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Re: 如何估计弱电破缺的能标
noether定理告诉我们,一个等度量变换导致一个守恒量.共形对称性导致什么守恒的量??
the trace of energy momentum tensor.
存在吗??
| 发表时间：2005-11-22, 09:11:26 |
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轩轩
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Re: 如何估计弱电破缺的能标
.共形对称性导致什么守恒的量??
the trace of energy momentum tensor.
这个trace是一个标量吧??? 为什么只一个受恒量?应该有5个呀.
witten有300多篇文章,评价他我用2个字:大文豪.
《相对论通俗演义》
i will love you till the null infinity.
| 发表时间：2005-11-22, 10:40:31 |
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卢昌海
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Re: 如何估计弱电破缺的能标
:: 这个trace是一个标量吧??? 为什么只一个受恒量?应该有5个呀.
The condition related to conformal symmetry is tracelessness of energy momentum tensor, this is pretty much what classical conformal symmetry implies. If you want to see conserved current, it is: C^{ab}=(2x^ax_c-x^2δ^b_c)T^{bc}. There isn't much new about the conservation of this current, it is a simple consequence of energy momentum conservation and symmetricity and tracelessness of the energy momentum tensor.
宠辱不惊，看庭前花开花落
去留无意，望天空云卷云舒
| 发表时间：2005-11-22, 18:25:11 |
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sage
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Re: 如何估计弱电破缺的能标
>he trace of energy momentum tensor.
>这个trace是一个标量吧??? 为什么只一个受恒量?应该有5个呀.
IT seems that you are not really interested in electroweak interactions. :-)
Anyway, let's talk about conformal transformations
Conformal group in d dimensions is a large group locally isomorphic to SO(p+1,q+1). SO(2,4) in our spacetime, for example.
Most of the generators are obvious ones such as translation and rotations. these has the usual conserved charges.
One the other hand, there is aslo a generator for a simple scaling. Its current is
\Theta_{mu nu}x^nu
where Theta_{mu nu} is the symmetrized energy-momentum tensor. The divergence of this current is proportional to the trace of the energy momentum tensor. It is conserved if the trace of energy momentun tensor vanishes.
the scaling transformation is especially important because its non-conservation captures the anomalous scaling of the operators. which is the renormalization group flow.
There is also a so-called special conformal transformation by inversion and translation. This shows that the fundamental space-time that a conformal theory is smaller than the full space-time.
In two dimensions, the conformal group is isomorphics to holomorphic functions, which is infinite dimensional. Therefore, virasoro algebra is infinite dimensional. its application in lower dimensional systems and string theory is well-known.
| 发表时间：2005-11-22, 21:29:14 |
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轩轩
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Re: 如何估计弱电破缺的能标
Conformal group in d dimensions is a large group locally isomorphic to SO(p+1,q+1). SO(2,4) in our spacetime, for example.
thanks sage
SO(2,4)是ADS5的等度量群,因此ADS5上的规范场论等价于M4上的共形场论??这个等价是在什么sense上说的??ADS5上的规范场论是什么规范场论呢?
witten有300多篇文章,评价他我用2个字:大文豪.
《相对论通俗演义》
i will love you till the null infinity.
| 发表时间：2005-11-23, 00:19:25 |
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sage
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Re: 如何估计弱电破缺的能标
SO(2,4)是ADS5的等度量群,因此ADS5上的规范场论
well, what gauge symmetry reflects the isometry of the background space? diffeomorphism! 'gauge theory' in AdS is the gravity in AdS.
as you said, it is equivalent to a CFT in M4. This is called AdS-CFT correspondence.
等价于M4上的共形场论??这个等价是在什么sense上说的??ADS5上的规范场论是什么规范场论呢?
| 发表时间：2005-11-23, 12:02:52 |
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