追忆
发表文章数: 693
武功等级: 般若掌
(第八重)
内力值: 463/463
Any questions about string theory
Ask for help:
1): In the String theory ,the back-ground of spacetime is not independent, it's very similar to that in classical Newton Mechanics, even is completely the same to that in classial case . and the general relativity tell us that the back-ground of spacetime should be independent. and spacetime should also depends on the particles itselves dynamics systems . How can we think of these ? (the conclussions which there two theories have showed are not consistent ,but of course,we have konwn what GR showed is correct )
As a theory of quantion Gravity ,if string theory is correct ,it has to satisfy the all argebral of QM and GR, now, we at most could only take the aproxiament for some calclutions and intepretion . it just say , when we consider something about string or sometime make use of it to discribe the course of interaction of particles ,we could only do it in the case that the back-ground of spacetime is aboslut.
2): How many the demensions does the universe which we are living in have ?whether this has been made a decision ,10 or 11?
For any different demensions ,there could be any very different types string theories for them .that in 9-D is the least ,only 5 types .
(well ,it's very late ,because of the limited time ,must stope here .something that has not been written well , next time i will continue ,ask for anybody's help for my recent study )
青山隐隐水迢迢，秋尽江南草木凋；
二十四桥明月夜，玉人何处教吹萧？
| 发表时间：2005-12-13, 13:56:57 |
 作者资料
|
季候风
发表文章数: 291
武功等级: 太极剑法
(第四重)
内力值: 370/370
Re: Any questions about string theory
我想现在的问题是这样。我们要或多或少“放弃”引力理论是背景无关的理论之一观点。再说离谱一点，“背景无关” 这个说法本身就是经典图像，背景无关实际上是度量无关，但是流形依然存在，只要有流形，就还是经典图像。如果我们放弃“时空流形”这个图像，那么就不会有度量，也就不会有“背景”。或者换句话说，我们可以离开时空谈论量子理论。只要一个量子理论的经典极限是 Einstein 理论，它就是量子引力。
弦论就是这么一个理论。在弦论中，代替时空背景的是共形场论背景。共形场论背景更加广泛，但是每一个满足 Einstein 方程的时空背景给出一个共形场论背景。这个过程类似于从一个经典理论得到一个量子理论的过程，实际上已经是 Einstein 理论的量子化了。
书山有路勤为径
学海无涯苦作舟
| 发表时间：2005-12-13, 21:36:05 |
作者资料
|
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: Any questions about string theory
我想现在的问题是这样。我们要或多或少“放弃”引力理论是背景无关的理论之一观点。再说离谱一点，“背景无关” 这个说法本身就是经典图像，背景无关实际上是度量无关，但是流形依然存在，只要有流形，就还是经典图像。如果我们放弃“时空流形”这个图像，那么就不会有度量，也就不会有“背景”。或者换句话说，我们可以离开时空谈论量子理论。只要一个量子理论的经典极限是 Einstein 理论，它就是量子引力。
弦论就是这么一个理论。在弦论中，代替时空背景的是共形场论背景。共形场论背景更加广泛，但是每一个满足 Einstein 方程的时空背景给出一个共形场论背景。这个过程类似于从一个经典理论得到一个量子理论的过程，实际上已经是 Einstein 理论的量子化了。
============================================================================
I don't know whether I understand what you mean.
String theory is background dependent. Every string theory we know how to deal with are defined in a particular background. It deals with the fluctuations around that background, including graviton excitations. It is at best an expansion around certain background, the expansion parameter is string length over curvature. On the other hand, there is no way to use that string theory to say something about the background itself when the background is highly non-trivial, for example, when the background curvature is larger than the length of the string.
Actually, it is also not true that every background statisfying the Einstein equation gives rise to conformal field theory.
| 发表时间：2005-12-13, 23:05:51 |
作者资料
|
季候风
发表文章数: 291
武功等级: 太极剑法
(第四重)
内力值: 370/370
Re: Any questions about string theory
呵呵，我刚才是班门弄斧了。我没有仔细看过弦论，关于弦论的信息来自于零散的文章。我想弦论本来是研究弦在时空中的运动，但是弦论三十年以后，很多人倾向于认为时空可能是弦运动的低能效应。而不是弦在“自在的”时空中运动。
你说不是每个 Einstein 背景都给出共形场论，具体是怎么回事？
书山有路勤为径
学海无涯苦作舟
| 发表时间：2005-12-14, 00:46:07 |
作者资料
|
季候风
发表文章数: 291
武功等级: 太极剑法
(第四重)
内力值: 370/370
Re: Any questions about string theory
不知道我这个理解对不对。g_{ij} 是共形场论的耦合常数，在低能的情况下场量表现为时空坐标而这个耦合常数表现为时空的度量。当然，如果说 g_{ij} 就是背景，那么弦论的确是背景有关的。我的理解是，“背景无关”这个说法本身就是旧观念，我们不应该执着于这个说法。“量子引力”为什么一定要是一个关于时空度量的理论呢？ 至少很多关心物理的数学家都相信弦论是量子引力理论。
书山有路勤为径
学海无涯苦作舟
| 发表时间：2005-12-14, 01:01:51 |
作者资料
|
kanex
发表文章数: 860
武功等级: 弹指神通
(第六重)
内力值: 343/343
Re: Any questions about string theory
关于"“量子引力”为什么一定要是一个关于时空度量的理论呢"，我想现在的确是有许多人同意的。for example，在lqg里面就看不到Guv和manifold的踪影。"时空可能是弦运动的低能效应"在witten的某个talk里看到过。
conformal field theory可以说是描述perturbative string theory中string worldsheet的理论，所以我也想听听为什么"不是每个 Einstein 背景都给出共形场论"。
"when the background curvature is larger than the length of the string"
我想量子效应是会“抹平”这种东西的吧。
江畔何人初见月`江月何年初照人`
| 发表时间：2005-12-14, 06:33:35 |
作者资料
|
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: Any questions about string theory
well, it is a long story. Let me try to sketch the answer.
In string theory, we start from an worldsheet action (called Poyakov action) which looks like
\int G_ij(X) d_a(X^i) d_b (X^j) + ... (other terms not does not involve metric)
ij is the so called target space (our space) coordinates. a and b are worldsheet coordinates. There could be a world sheet metric as well but it could be diff away.
At this point, X_i s are worldsheet quantum fields as functions of a and b. This is a hopeless action to solve since G_ij depend on X, which is highly non-linear. Therefore, even if for no reason this action indeed captures all the effects of quantum gravity, there is no way to solve it.
Now, the only way we can get something is to expand that action in some background. By background, in this case, we mean giving vacuum expectation values to field X_i.
That is <X_i>=x_i, where x_i has the interpretation of the classical coordinates.
We can then expand by
X_i=x_i+y_i
where y_i is the quantum fluctuation around x_i. Now, the action turns into a action of y_i in the background of G_ij(x_i). This is the background dependence of string theory. It does not dynamically generate a background, in general. It is still true that for general background, it is a very hard to solve theory. on the other hand, one can at least imagine it is doable in some local neighbourhood since we can always make things locally flat.
Looking at higher order expansions, you see terms of the form
(G_ij, kl) y^k y^l d_a y^i d_b y^j+..... which is of the form
Riemann tensor \times y^2 dy dy
Since the natural size of y is the size of the strings, this show us the expansion parameter here is actually
[(size of string)/(radius of curvature)]^2
which actually breaks down at the point where the curvature is close to string scale.
Therefore, being a background dependent theory, it breaks down at the scale where the quantum gravity effect is large and classical background is no longer good.
--------------------------------------------------------------------------------------------------------
Now the question of conformal invariance. The classical gauge symmetry for the action is the worldsheet diff and conformal invariance, there is also a global symmetry which is the target space diffeomorphism. Now, you can show that you could use all of these symmetry to massage that action (after expand around a flat background) into a 2D conformal field theory. On the other hand, this is in general only true classically. There is a worldsheet conformal anomaly which tells us whether one can do this depends on the background. The requirements are
1) locally, the fluctuation of the background has to satisfy Einstein equation.
2) the number of dimensions has to be a particular number to cancel conformal anomaly. For example, for bosonic string, it has to be 26. for superstring, it has to be 10.
| 发表时间：2005-12-14, 20:31:26 |
作者资料
|
yinhow
发表文章数: 727
武功等级: 弹指神通
(第二重)
内力值: 469/469
Re: Any questions about string theory
That is <X_i>=x_i, where x_i has the interpretation of the classical coordinates.
================================================
为了计算方便，可以用测地线坐标（s）展开。quantum fluction y的一阶项总能消掉，
L作用量里只保留最低的二阶项， 写成y.P. y的形式，P是复杂的算符。
| 发表时间：2005-12-14, 20:42:41 |
作者资料
|
季候风
发表文章数: 291
武功等级: 太极剑法
(第四重)
内力值: 370/370
Re: Any questions about string theory
sage, 非常感谢你的解释。那么你认为弦论是量子引力吗？
书山有路勤为径
学海无涯苦作舟
| 发表时间：2005-12-14, 21:41:11 |
作者资料
|
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: Any questions about string theory
sage, 非常感谢你的解释。那么你认为弦论是量子引力吗？
-------------------------------------------------------------------------------
it depends on what you mean by quantum gravity. string theory, or pterturbative string theory, is quantum gravity in the sense that in a given background, it captures the full quantum effect of gravitons. and it is finite.
On the other hand, depsite some limited success, it does not do quantum gravity in the extreme conditions where the concept of a background breaks down, such as big bang singularity or center of the blackhole. Therefore, string theorists have been working very hard to find non-trivial solutions of string theory or other ways of understanding string theory in those conditions. no big success yet.
fundamentally, nobody knows what the basic degrees of freedom are in a true quantum gravity. It could be strings, it could be something else as well. It could be metric as well.
String theory, so far, is the best candidate for a quantum gravity, although a lot still need to be done.
Nothing else is even close yet.
| 发表时间：2005-12-14, 21:58:52 |
作者资料
|