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  本文關鍵詞：膜世界中的物質場及其KK模式　出處：《蘭州大學》2013年博士論文　論文類型：學位論文

  更多相關文章： 額外維 膜世界 KK模式

【摘要】：膜世界理論的提出,為解決層次問題、宇宙學常數(shù)等難題提供了新的思路,因而倍受關注.本文將著重研究膜世界中的物質場及其KK模式,研究目的是通過分析膜世界中物質場的KK模式,提供一種理論上驗證膜世界理論的方法。 膜世界理論,先后經歷了薄膜和厚膜的發(fā)展階段.初期階段的膜世界理論是薄膜理論,如ADD理論、RS理論.這兩種理論,著重解決了層次問題,至此也揭開了膜世界理論發(fā)展的序幕.不過薄膜理論忽略了膜本身的厚度,是數(shù)學上的一種理想化,而現(xiàn)實的膜是應該有厚度的,因而厚膜理論得到了發(fā)展。在厚膜理論中,通過引入背景標量場,使得膜的能量密度沿額外維有了一定的展寬.不過因為沒有限定標量勢的具體形式,所以厚膜世界解具有多樣性. 膜世界理論認為,標準模型中的粒子都被束縛在膜上,引力可以在膜之外的時空傳播。因此,需要一種可以使得這些物質場自然地束縛在膜上的機制.同時,這樣才能保證膜世界理論不與現(xiàn)實的世界相矛盾,這也是現(xiàn)實的膜世界模型首先要保證的。本文重點探討一種使得物質場能夠被束縛在膜上的機制,即局域化機制。 另外,在膜世界理論中,時空的維度是大于四維的,即有額外的空間維度存在。那么如何驗證額外維存在的真實性也成了一個重要的科研問題。事實上,額外維理論的發(fā)展是早于膜世界理論的,不過膜世界理論的提出為驗證額外維的真實存在性提供了一個重要的方法,就是上文提到的膜世界中物質場的局域化。 通過物質場的局域化方法,我們可以得到這些物質場的KK模式。所謂的KK模式,是指高維時空中的物質場在低維膜上的表現(xiàn)形式。因此,這種KK模式必然隱含了高維時空(額外維空間)的性質,并通過質量表現(xiàn)出來。于是,通過分析物質場的KK模式的質量譜,就可以了解到高維時空的性質。 在研究的過程中,我們還發(fā)現(xiàn)一些特殊的模式(零模)。利用一定的局域化條件,可以使得它們被束縛在膜上.被束縛在膜上的零模式,與額外維無關,不受額外維的影響,因此可以認為這些模式代表著膜上已知的物質場。這樣就實現(xiàn)了自然地局域化膜上已知物質場的目的,由此,可以看出研究膜世界中的物質場及其KK模式的重要性.而KK模式的質量譜是依賴于不同的膜世界模型的。 本文重點討論了三種有趣的膜世界模型中的物質場及其KK模式。首先,討論了五維時空中的GRS-inspired膜世界中的情況,這種膜的特點是薄膜和厚膜同時存在.標量場和費米場的零模解都可以被束縛在該膜上,并且存在有質量的束縛態(tài)和共振態(tài)KK模式。不過矢量場卻不能被束縛在這種膜世界中。于是,我們針對矢量場的局域化問題,提出額外維有限的厚膜世界模型(包括單膜和劈裂膜).在這中膜世界模型中,我們借助額外維的有限性使得矢量場也能夠被局域化在膜上。最后,我們將膜世界理論從五維推廣到任意維膜世界,即p—膜世界,求解出幾種具有代表性的p—膜世界解。同時研究了這些模型中任意q—形式場的局域化問題,發(fā)現(xiàn)了膜的空間維數(shù)p對于不同的q—形式場局域化的影響,所得到的關于標量場(q=0)、矢量場(q=1)的局域化結果不僅與五維時空中的情況相吻合,還給出了一些新的預言。 但是,本文所采用的局域化機制只能從理論上驗證膜世界理論的合理性(使得膜上已知的物質場自然地束縛在膜上)與真實性(額外維的存在性).而通過進一步地計算引力的KK模式對于牛頓勢的修正,或規(guī)范場的KK模式對于庫倫勢的修正,就可以尋求實驗上驗證的可能性,這也是我們的下一步工作。
[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.

【學位授予單位】：蘭州大學
【學位級別】：博士
【學位授予年份】：2013
【分類號】：O412;P159

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