膜世界中的物质场及其KK模式

发布时间：2018-01-05 04:06

本文关键词：膜世界中的物质场及其KK模式　出处：《兰州大学》2013年博士论文　论文类型：学位论文

【摘要】：膜世界理论的提出,为解决层次问题、宇宙学常数等难题提供了新的思路,因而倍受关注.本文将着重研究膜世界中的物质场及其KK模式,研究目的是通过分析膜世界中物质场的KK模式,提供一种理论上验证膜世界理论的方法。膜世界理论,先后经历了薄膜和厚膜的发展阶段.初期阶段的膜世界理论是薄膜理论,如ADD理论、RS理论.这两种理论,着重解决了层次问题,至此也揭开了膜世界理论发展的序幕.不过薄膜理论忽略了膜本身的厚度,是数学上的一种理想化,而现实的膜是应该有厚度的,因而厚膜理论得到了发展。在厚膜理论中,通过引入背景标量场,使得膜的能量密度沿额外维有了一定的展宽.不过因为没有限定标量势的具体形式,所以厚膜世界解具有多样性. 膜世界理论认为,标准模型中的粒子都被束缚在膜上,引力可以在膜之外的时空传播。因此,需要一种可以使得这些物质场自然地束缚在膜上的机制.同时,这样才能保证膜世界理论不与现实的世界相矛盾,这也是现实的膜世界模型首先要保证的。本文重点探讨一种使得物质场能够被束缚在膜上的机制,即局域化机制。另外,在膜世界理论中,时空的维度是大于四维的,即有额外的空间维度存在。那么如何验证额外维存在的真实性也成了一个重要的科研问题。事实上,额外维理论的发展是早于膜世界理论的,不过膜世界理论的提出为验证额外维的真实存在性提供了一个重要的方法,就是上文提到的膜世界中物质场的局域化。通过物质场的局域化方法,我们可以得到这些物质场的KK模式。所谓的KK模式,是指高维时空中的物质场在低维膜上的表现形式。因此,这种KK模式必然隐含了高维时空(额外维空间)的性质,并通过质量表现出来。于是,通过分析物质场的KK模式的质量谱,就可以了解到高维时空的性质。在研究的过程中,我们还发现一些特殊的模式(零模)。利用一定的局域化条件,可以使得它们被束缚在膜上.被束缚在膜上的零模式,与额外维无关,不受额外维的影响,因此可以认为这些模式代表着膜上已知的物质场。这样就实现了自然地局域化膜上已知物质场的目的,由此,可以看出研究膜世界中的物质场及其KK模式的重要性.而KK模式的质量谱是依赖于不同的膜世界模型的。本文重点讨论了三种有趣的膜世界模型中的物质场及其KK模式。首先,讨论了五维时空中的GRS-inspired膜世界中的情况,这种膜的特点是薄膜和厚膜同时存在.标量场和费米场的零模解都可以被束缚在该膜上,并且存在有质量的束缚态和共振态KK模式。不过矢量场却不能被束缚在这种膜世界中。于是,我们针对矢量场的局域化问题,提出额外维有限的厚膜世界模型(包括单膜和劈裂膜).在这中膜世界模型中,我们借助额外维的有限性使得矢量场也能够被局域化在膜上。最后,我们将膜世界理论从五维推广到任意维膜世界,即p—膜世界,求解出几种具有代表性的p—膜世界解。同时研究了这些模型中任意q—形式场的局域化问题,发现了膜的空间维数p对于不同的q—形式场局域化的影响,所得到的关于标量场(q=0)、矢量场(q=1)的局域化结果不仅与五维时空中的情况相吻合,还给出了一些新的预言。但是,本文所采用的局域化机制只能从理论上验证膜世界理论的合理性(使得膜上已知的物质场自然地束缚在膜上)与真实性(额外维的存在性).而通过进一步地计算引力的KK模式对于牛顿势的修正,或规范场的KK模式对于库伦势的修正,就可以寻求实验上验证的可能性,这也是我们的下一步工作。
[Abstract]:The film theory of the world, in order to solve the problems, provides a new way to the cosmological constant problem, it has attracted considerable attention. This paper will focus on the material field and the KK model of film in the world, the research purpose of this paper is to analyze the world in the field of membrane material KK model, provides a method to verify the theory on world film theory.
The theory of film world, has experienced the development stage of thin and thick films. The early stage of the world film theory and film theory, such as ADD theory, RS theory. These two theories, focusing on solving the problem of level, this is a prelude to the development of the world. But the theory of film film theory ignores the thickness of the film itself, is a kind of ideal in mathematics, but the reality is there should be a film thickness, and film theory has been developed. In the thick film theory, by introducing the background of scalar field, the membrane energy density along the extra dimension of a certain width. But because of the specific form of the scalar potential is not limited, so thick film world the solution has diversity.
According to the theory of film world, the standard model of particle bound on the film, propagating on membrane outside gravity. Therefore, the need for a mechanism that these substances field naturally bound in the membrane. At the same time, so as to ensure that the film world and the reality of the theory of world conflict, it is the reality of the film world model must be guaranteed first. This paper focuses on a mechanism allowing the material field can be bound in the membrane, namely localization mechanism.
In addition, in the theory of film world, space-time dimension is greater than four, namely the existence of extra dimensions. So how to verify the authenticity of the extra dimension have also become an important research problem. In fact, the development of the extra dimension theory is earlier than the membrane theory of the world, but put forward the theory of film the world in order to verify the existence of extra dimension provides an important method, is the material field mentioned above in the film world localization.
The localization method of material field, we can get the material field of the KK model. The so-called KK model, refers to the form of high dimensional space in the material field in the low dimensional membrane. Therefore, this KK model implied high dimensional space (extra dimensions) properties, and through quality performance come out. Then, through the analysis of the quality of material field of KK mode spectrum, we can understand the nature of the high dimensional space.
In the course of the study, we also found some special mode (zero mode). The use of certain localization conditions, can make them trapped in the membrane. The zero mode is bound to the membrane, has nothing to do with the extra dimension, is not affected by the extra dimension, so that these patterns represent the membrane material field known. This has known material field naturally localized on the membrane, which can be seen, the importance of material field and KK model of film in the world. The quality of KK mode spectrum is dependent on the different film world model.
This paper focuses on the three film world model interesting material in the field of KK mode. Firstly, discussed the GRS-inspired film in the world five dimensional space, characteristic of the film is thin and thick films exist at the same time. The zero mode scalar and fermion field solution can be bound on the film, and there is a quality bound and KK resonance mode. But the vector field cannot be bound in the film world. So, we aimed at the localization of the vector field problem, the thick film world model extra dimension Limited (including single film and split film). In this film in the world model, we use finite the extra dimension vector field can be localized in the membrane. Finally, we will extend to the world from the fifth film theory of arbitrary dimensional film world, namely p - film world P film world for several representative research and the solution. The localization problem of arbitrary Q - form model in some field, found the film space dimension P for different Q form field localization, obtained on the scalar field, vector field (q=0) (q=1) and the localization results not only in five dimensional space coincides with the situation, some new prediction is given.
However, only the localization mechanism theoretically verifies the rationality of the world (the theory of membrane membrane known material field naturally bound in the film) and reality (the existence of extra dimension). Through further calculation of gravity KK model for the modified Newton potential, modify or gauge field KK model for Kulun potential, you can seek the possibility of experimental verification, this is the next step in our work.

【学位授予单位】：兰州大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：O412;P159

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