kanex
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请大家看看我对于QFT的这种理解有无错误
Basically, we can formulate QFT in three different ways:
1) Creation & Annihilation Operator + Fock space
2) Field + Path Integral
3) Particle + “Feynman Diagram”-like process [I don’t know what the exact name for this is, nor did I see it in any books]. I find this approach the least confusing. But it should be handled with great care. Basically this is my standpoint.
Firstly, we shall make it clear what is the vacuum state [please forget about all the subtlety such as the symmetry breaking, the degeneration of vacuum, and the impossibility of defining it near the big bang]. It is |0> in 1), 0 in 2), and the null set in 3).
If we apply the creation operator to the vacuum, we get a particle with some determined momentum, which is a vector in the Fock space in 1), a plane wave in the field in 2), and a point in the spacetime in 3).
Now I am sure that this will make experts in QFT angry: how can I have a “fixed” point in the spacetime, if I know the momentum of the particle exactly? That’s exactly where the confusion lies. QFT = SR + QM. From principle of relativity, it is impossible to choose a “fixed” point in spacetime. If we moduli the arbitrariness of defining the coordinates, or the arbitrariness of finding a “point” in spacetime for our particle, we know exactly nothing on the position of the particle. So you see, this does not violate the uncertainty principle at all.
I hope I succeeded in making the issue clear.
江畔何人初见月`江月何年初照人`
| 发表时间：2005-12-12, 22:02:20 |
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kanex
发表文章数: 860
武功等级: 弹指神通
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Re: 请大家看看我对于QFT的这种理解有无错误
I am happy with my idea.
It seems that it will lead to something very deep and exciting if we want to combine QM with GR.
江畔何人初见月`江月何年初照人`
| 发表时间：2005-12-12, 22:05:24 |
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季候风
发表文章数: 291
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Re: 请大家看看我对于QFT的这种理解有无错误
I do think the three items you listed are different aspects of QFT, not three ways of QFT. Have you read Weinberg's book (vol I)? This book will help you to clear all these.
书山有路勤为径
学海无涯苦作舟
| 发表时间：2005-12-12, 23:21:10 |
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kanex
发表文章数: 860
武功等级: 弹指神通
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Re: 请大家看看我对于QFT的这种理解有无错误
In my opinion they are three isomorphic categories.
江畔何人初见月`江月何年初照人`
| 发表时间：2005-12-12, 23:50:13 |
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季候风
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Re: 请大家看看我对于QFT的这种理解有无错误
OK. Let's discuss your proposal,
~~~~~~~~~~~~~~~~~~~~~~~~~
From principle of relativity, it is impossible to choose a “fixed” point in spacetime. If we moduli the arbitrariness of defining the coordinates, or the arbitrariness of finding a “point” in spacetime for our particle, we know exactly nothing on the position of the particle. So you see, this does not violate the uncertainty principle at all.
~~~~~~~~~~~~~~~~~~~~
I don't understand the logic here. Maybe you can use Chinese in order to make your thoughts more clear. As far as I know, a point in spacetime is just an event, it is well-defined in the special relativity. Why did you say it is impossible to choose a "fixed" point in spacetime?
书山有路勤为径
学海无涯苦作舟
| 发表时间：2005-12-13, 00:10:42 |
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sage
发表文章数: 1125
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Re: 请大家看看我对于QFT的这种理解有无错误
First of all, I agree with Ji Hou Feng that they are really that different, but equivalent in the sense that they give identical physical predictions, which is the only thing that matters in physics.
Second, i do not see anything that is new.
Third, I strongly suggest you do not send this to Li Miao, he will definitely treat you as a crackpot. if you are applying for grad school or something else, do not write this into the research interest.
Fourth, a personal suggestion, you of course could ignore this. This is probably not something that you should work on. Attempts to "really understand" field theory have been
going on for many years under various names. It never has lead to any useful insight.
Now, I have a few comments on what you have said below.
------------------------------------------------------------------------
>Basically, we can formulate QFT in three different ways:
>1) Creation & Annihilation Operator + Fock space
>2) Field + Path Integral
>3) Particle + “Feynman Diagram”-like process [I don’t know what the exact name for this >is, nor did I see it in any books]. I find this approach the least confusing. But it should be >handled with great care. Basically this is my standpoint.
-----------------------------------------------------------------------------------
The third one is probably close to the so called S-matrix approach which has been studied about 30 years ago. It is either identical to the first two, or not useful without the first two.
----------------------------------------------------------------------------
>Firstly, we shall make it clear what is the vacuum state [please forget about all the >subtlety such as the symmetry breaking, the degeneration of vacuum, and the >impossibility of defining it near the big bang]. It is |0> in 1), 0 in 2), and the null set in 3).
as I said, there is no difference in vacuum state here. The difference is only language. There is a nicely defined operator-state mapping between pathinegral and state in the fock space.
>If we apply the creation operator to the vacuum, we get a particle with some determined >momentum, which is a vector in the Fock space in 1), a plane wave in the field in 2), and >a point in the spacetime in 3).
>Now I am sure that this will make experts in QFT angry: how can I have a “fixed” point in >the spacetime, if I know the momentum of the particle exactly? That’s exactly where the >confusion lies. QFT = SR + QM. From principle of relativity, it is impossible to choose a >“fixed” point in spacetime. If we moduli the arbitrariness of defining the coordinates, or >the arbitrariness of finding a “point” in spacetime for our particle, we know exactly nothing >on the position of the particle. So you see, this does not violate the uncertainty principle >at all.
the last paragraph is probably wrong. uncertainty in position measurement cannot come from and does not follow from special relativity.
Again, whatever you do in any new formulation of field theory, it will only useful if one of followings is true
1) it is not equivalent to field theory. in the case, it is your responsibility to point a experiment that can distinguish them.
2) it is equivalent to field theory. in this case, it is your responsibility to prove they are equivalent, and it is not one of the old approaches, and most importantly, why is this approach useful (by carry out a calculation in this approach which is not doable in the old approach)
only when you satisfy these conditions, people will start even look at your stuff.
by reading this or your earlier post, I think I understand why Li Miao think you are a crackpot.
I hope I succeeded in making the issue clear.
| 发表时间：2005-12-13, 00:59:02 |
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星空浩淼
发表文章数: 1743
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Re: 请大家看看我对于QFT的这种理解有无错误
我英文差，就用中文说两句自己知道的：
“Basically, we can formulate QFT in three different ways:
1) Creation & Annihilation Operator + Fock space
2) Field + Path Integral
3) Particle + “Feynman Diagram”-like”
如果一定要找出三种不同途径，那第三种应该是“几何量子化”，这个要用到辛几何，一般人可能不愿意去花大力气去了解这种办法，毕竟它涉及的数学比较深，比另外两种难懂多了。而且它也许在物理计算方面并不实用，除非为了向更一般理论推广（因为几何量子化不依赖于表象）。
第一种就直接称作是正则量子化方法吧。至于上述第三点，前面他们已经指出，它只能算属于1）和2）中都要用到的具体技巧。
几句话外题：上面sage兄有些话虽然听起来似乎比较严重不中听，其实很中肯很有帮助。有些东西等到若干年以后，才能明白长辈们的良苦用心。sage兄在这里对于任何人都是一样的，是对事不对人，这一点我都不能完全做到。
在这里，我每次发贴，既希望sage兄看到又害怕sage兄看到（在这里能让我怕的人不多），呵呵！自己的帖子被人挑刺，要比没有人理好上万倍。
我在故我寻，我寻故我痴；我痴故我呆，我呆故我笨；我笨故我傻，我傻故我贫；我贫故我苦，我苦故我悲；我悲故我思，我思故我在，我在故我寻
| 发表时间：2005-12-13, 04:10:25 |
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季候风
发表文章数: 291
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Re: 请大家看看我对于QFT的这种理解有无错误
几何量子化只是数学家为了理解正则量子化而提出的数学模型，不过的确涉及很深奥的数学。这种研究也促进了辛几何和复几何的研究。
书山有路勤为径
学海无涯苦作舟
| 发表时间：2005-12-13, 04:16:19 |
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kanex
发表文章数: 860
武功等级: 弹指神通
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Re: 请大家看看我对于QFT的这种理解有无错误
Dear sage,
非常感谢。
我之前向李淼教授写信的时候一上来就用第三种，所以后果严重－－看上去根本不像是对量子力学有什么理解。
I have seen axiomatic field theory. It is simply too general... so general that it is not very useful.
I know S-matrix. In some sense they are quite close. But S-matrix think that the matrix can be determined solely from symmetries, which is leading nowhere. 第三种的好处是很干净。是的都等价。
我想的是从某种广义的等效原理推出QM的可能性，然而离接近非常远，所以才只写了一点就卡壳了。
sage老师，之前对您有些无心的不敬之语，星空兄提醒了我才想到，敬请原谅。
我已打算放弃申请，因平时成绩实在很差。
我的确是民科，一点没错。我的计算能力极度低下〔看书时对于计算部分看得太慢，只好硬着头皮跳过去〕，用语更是极不规范，跳来跳去。造成的误会众多，大家也都见识过。
我长久以来的梦想是量子引力。然而接触得越多，越发感到自己的无力与苍白。这就是所谓志大才疏吧，真的没救了。
江畔何人初见月`江月何年初照人`
| 发表时间：2005-12-13, 09:47:25 |
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kanex
发表文章数: 860
武功等级: 弹指神通
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Re: 请大家看看我对于QFT的这种理解有无错误
There is also deformation quantization, which is difficult as well.
江畔何人初见月`江月何年初照人`
| 发表时间：2005-12-13, 09:50:17 |
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季候风
发表文章数: 291
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(第四重)
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Re: 请大家看看我对于QFT的这种理解有无错误
有理想，或者说有梦想是好的，但是也要认识到这个世界上有成千上万资质既高，用功又勤的物理数学工作者，他们在思考同一问题。能提出新理论的人，首先，对之前种种办法为什么行不通要有非常深刻的认识。以现在物理和数学的发展程度，博士毕业都只能算是初窥门径，所知不过是沧海一粟，怎么能够奢谈对世界的终极理论有新的见解？
从另一个方面来说，做学问有个大的目标是好的。现今社会，生存是第一位的。在谋生的过程中，可能会习惯于随波逐流。为了前途，可能要在你没有兴趣的课程里拿个好分数，可能要在你觉得无聊的热门方向写几篇垃圾文章。有的人做着这些事情，不知不觉就做成习惯了。阻止你形成这种习惯的就应该是永无穷尽的求知欲。在维护生存权利的过程中，要保留一颗孩童的心，好奇心。但是，不能把对终极理论的梦想作为逃避现实的借口，要为自己争取一个安静的研究环境，你就必须在学校拿到好分数，在研究生阶段做一些小课题，而把你的梦想留给将来。
书山有路勤为径
学海无涯苦作舟
| 发表时间：2005-12-13, 20:19:08 |
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yinhow
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Re: 请大家看看我对于QFT的这种理解有无错误
我的计算能力极度低下
=============
除了expert以外，大家的计算能力差不多
| 发表时间：2005-12-13, 20:55:02 |
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sage
发表文章数: 1125
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Re: 请大家看看我对于QFT的这种理解有无错误
我想的是从某种广义的等效原理推出QM的可能性，然而离接近非常远，所以才只写了一点就卡壳了。
========================================================================
This sounds like a very remote possibility. there seems to be no evidence that it would work. therefore, it is something better to think about in your spare time.
>sage老师，之前对您有些无心的不敬之语，星空兄提醒了我才想到，敬请原谅。
===================================================================
I did not noticed anything. therefore, don't worry about it...
>我已打算放弃申请，因平时成绩实在很差。
=====================================================================
Well, you should not. transcript is not necessarily the most important thing in order for people to be interested in you. It is more important for you to try to establish some connections. Contacting Li Miao is a good idea since he is good and he has connections. On the other hand, you have to pay attention to your method.
我的确是民科，一点没错。我的计算能力极度低下〔看书时对于计算部分看得太慢，只好硬着头皮跳过去〕，用语更是极不规范，跳来跳去。造成的误会众多，大家也都见识过。
======================================================================
skipping calculations is not necessarily bad. the most important thing is the understanding of concepts, not really the ability to calculate. Of course, many key concept can only be understood once you go through it.
A lot of the fancy stuff is quite useless. on the other hand, the basic points of quantum field ttheory are behind everything that we are doing today, including string theory. Therefore, it worthwhile to spend a lot of time just on the basics of quantum field theory.
我长久以来的梦想是量子引力。然而接触得越多，越发感到自己的无力与苍白。这就是所谓志大才疏吧，真的没救了。
Quantum gravity is a dream for many people. Nobody really understand it yet.. Therefore, you do have to feel discouraged at all. It is better to start with small things first. big discoveries are usually not from some big vision, rather from simple examples.
| 发表时间：2005-12-13, 21:46:56 |
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sage
发表文章数: 1125
武功等级: 天山六阳掌
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Re: 请大家看看我对于QFT的这种理解有无错误
几句话外题：上面sage兄有些话虽然听起来似乎比较严重不中听，其实很中肯很有帮助。有些东西等到若干年以后，才能明白长辈们的良苦用心。sage兄在这里对于任何人都是一样的，是对事不对人，这一点我都不能完全做到。
在这里，我每次发贴，既希望sage兄看到又害怕sage兄看到（在这里能让我怕的人不多），呵呵！自己的帖子被人挑刺，要比没有人理好上万倍。
====================================================================
Thank you for the understanding. :-)
| 发表时间：2005-12-13, 22:59:04 |
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walk_f