星空浩淼
发表文章数: 1743
武功等级: 九阳神功
(第五重)
内力值: 617/617
回yinhow兄
“受楼主启发, 也天马行空瞎想: 相变->Euclidean空间变到Minkowski空间(对称打破)->虚时间(温度)->虚质量->虚引力子->温度引力场->熵.
温度一方面是体系平均能量(动能)的体现, 是否也可以是某个对称破缺的标志?零温有对称性, 无穷大温度(极高温)有另一种对称性, 可偏偏中间部位对称性不高.
经典的热力学理论中温度和熵是一对偶量, 按时行的语言来说, 量子相变是和某个拓扑量联系起来的. 黑洞的熵也可以看作是 拓扑量, 不是时空流形上的, 而是某个相空间上的. ”
呵呵，类似的联想很多，许多大科学家在这些方面浮想联翩
量子统计物理和量子场论之间有如下类比或对应：
组态求和——Feynman路径积分
配分函数——生成泛函
自由能密度——真空能量密度
关联函数——虚时传播子
关联长度的倒数——质量隙
高温/低温展开——强耦合/弱耦合展开
相变——相变（对称破缺）
...
不知其他人有何看法？
持之以恒就是胜利
| 发表时间：2004-11-04, 10:44:11 |
 作者资料
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sage
发表文章数: 1125
武功等级: 天山六阳掌
(第六重)
内力值: 535/535
Re: 回yinhow兄
Finite temparature system has less space-time symmetry comparing with zero temparature case. For example, it will choose a frame of increasing entropy (the most obvious example is the expansion of our universe). It also breaks supersymmetry which is kind of a extended space-time symmetry.
In terms of internal symmetrys (such as gauge symmetry), it is really a dynamical question how the symmetry of the system varies with time. For exmaple, it has been shown that certain gauge symmetry could be restored by going to high temparature. It is the same story as phase transition.
| 发表时间：2004-11-04, 14:10:12 |
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轩轩
发表文章数: 1352
武功等级: 易筋经
(第二重)
内力值: 567/567
Re: 回yinhow兄
星空，sage兄，举重如轻，让我学到不少东西
据说，在宇宙暴涨的时候，宇宙象De-sitter，具有最大对称，外耳退化，penrose用外耳的自我缩并来定义熵。后来，De-sitter变成了RW，……熵增加，简单地说，从De-sitter变成RW，需要什么条件？
什么是相变？
http://zhangxuanzhong.blogone.net
我的主页
(2004-06-01 13:58:27) 轩轩
super star
| 发表时间：2004-11-04, 23:03:52 |
作者资料
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sage
发表文章数: 1125
武功等级: 天山六阳掌
(第六重)
内力值: 535/535
Re: 回yinhow兄
De Sitter phase means we have a positive vacuum energy (or positive cosmological constant), it will generate a spacetime with constant curvature. It could happen, for example, if the energy in the universe is dominated by a scalar field which is trapped in a quasi-stable vacuum with potential energy >0. Or, as the most popular point of view, the potential have a long but very small slope so that the scalar field spends a lot time on that slope. During that period of time, V>0
After inflation, the spacetime is flat with a FRW metric. The transition could happen, for example, as the slope mentioned above come to an end and the field suddenly slide down to the bottom of a deeper well with vacuum energy =0
| 发表时间：2004-11-04, 23:18:53 |
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