kanex
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QED中有什么有解析解的计算么
验证一个不成熟的想法。直接比较解析形式难度很大，只能算点东西比较一下。
纯photon的问题应该有解析解吧？
江畔何人初见月`江月何年初照人`
| 发表时间：2005-05-13, 15:22:20 |
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卢昌海
发表文章数: 1617
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Re: QED中有什么有解析解的计算么
Depends on what do you mean by "解析解"? If you mean exact solution or non-perturbative solution. The answer seems to be "No". In fact, some researchers have claimed that 4-D QFTs that are not asymptotically free (QED included) all have trivial S-matrix (therefore there is no non-trivial scattering process) if no cut-off is present. This is called the triviality problem. It is not conclusive according to some physicists (for instance S. Weinberg). But the mere fact that it is NOT conclusively abandoned yet means we don't know any non-trivial non-perturbative solution in those QFTs (otherwise the triviality problme would have been abandoned already).
If you mean analytical solution at a given perturbation level, then there are numerous such solutions (all tree level calculations, all 1-loop calculations that can be expressed in closed forms, etc).
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：2005-05-13, 19:48:07 |
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No-go
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Re: QED中有什么有解析解的计算么
I heard that there are exact analytical solutions in 2D field theory.
| 发表时间：2005-05-13, 22:54:20 |
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卢昌海
发表文章数: 1617
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Re: QED中有什么有解析解的计算么
:: I heard that there are exact analytical solutions in 2D field theory.
That is true. In QED_2, massless case (aka massless Schwinger model) is known to be exactly solvable. I'm not sure whether any exact solution has been found for the massive case (namely with massive fermion).
There are other exactly solvable 2D QFTs as well.
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：2005-05-14, 07:03:53 |
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权权
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Re: QED中有什么有解析解的计算么
Then what about the triviality problem in 2-D case?
不忧不惧
| 发表时间：2005-05-14, 13:26:06 |
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卢昌海
发表文章数: 1617
武功等级: 北冥神功
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Re: QED中有什么有解析解的计算么
:: Then what about the triviality problem in 2-D case?
I never seen anyone discussed the complete scope of triviality problem. What I mentioned in the earlier post is only for 4D.
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：2005-05-14, 17:45:46 |
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星空浩淼
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Re: QED中有什么有解析解的计算么
凡是非线性问题，都很难有解析解。能够有的那些类型，可能在非线性物理中人们已经研究清楚了，剩下的那些，多半是没有的。
纯光子问题，如果没有涉及任何相互作用，例如不涉及光子内部部分子结构问题，不涉及光子-光子散射等QED相互作用，应该是线性的吧。
唯有与时间赛跑，方可维持一息尚存
| 发表时间：2005-05-15, 00:23:26 |
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walk_f
