膜世界中引力微子場和規(guī)范場的局域化
發(fā)布時間：2018-12-13 06:14
【摘要】：額外維與膜世界理論由于能夠解決物理學(xué)中的基本難題,如規(guī)范層次問題、宇宙學(xué)常數(shù)問題等,因而備受關(guān)注。在膜世界理論中,一個非常重要的課題就是研究高維時空中的各種物質(zhì)場局域在膜上的機制,從而實現(xiàn)四維膜上粒子物理標(biāo)準(zhǔn)模型的重構(gòu),并為未來的實驗提供指導(dǎo)。此外,暗物質(zhì)問題已成為當(dāng)前物理學(xué)的前沿課題之一,而在超對稱理論中引力微子場是引力子的超對稱費米型伴隨粒子,被認(rèn)為是暗物質(zhì)的候選者之一。本論文將重點研究五維膜世界理論中引力微子場和規(guī)范場(Kalb-Ramond(KR)場和矢量場)在薄膜及厚膜上的局域化性質(zhì)。本論文中,我們首先回顧額外維理論以及膜世界理論的發(fā)展歷程,并介紹了KK理論和幾種主要的膜世界理論(包括著名的Arkani-Hamed-Dimopoulos-Dvali(ADD)模型、Ra-ndall-Sundram(RS)模型以及標(biāo)量張量膜世界模型)。其中ADD和RS模型都是薄膜模型,主要解決規(guī)范層次問題,從而揭開了膜世界理論的序幕。然而,薄膜模型是一種忽略膜厚度的理想模型。考慮現(xiàn)實的有厚度的膜進(jìn)一步促使了厚膜理論的提出和膜世界的發(fā)展。在厚膜理論中,通過引入背景標(biāo)量場來作為構(gòu)造厚膜的物質(zhì)場,使得膜的能量密度沿額外維有了一定的分布。由于構(gòu)建厚膜的標(biāo)量場沒有限定具體的形式,從而厚膜膜世界解具有多樣性。其次,我們研究了五維有質(zhì)量的引力微子場在額外維具有S1/Z2拓?fù)淙毕莸谋∧つＰ?RS和標(biāo)量張量膜世界模型)中的局域化性質(zhì)。研究表明,(i)對于RS模型,存在膜上無質(zhì)量的手征模式以及一系列有質(zhì)量的Kaluza-Klein(KK)手征束縛態(tài),且在物理坐標(biāo)下一些較低能級的KK手征模式均束縛在TeV膜附近；(ii)對于標(biāo)量張量膜世界模型(考慮兩種解),模型參數(shù)λ的大小決定著無質(zhì)量手征模式的局域化性質(zhì),且引力微子的質(zhì)量譜和局域化性質(zhì)對這兩種解是不同,表明了這兩種解在物理上是不等價的。接著,第三章中我們通過引入了一種特殊耦合形式f(φ(z))=e(-7-2p)A(z)(p-9/2)來研究KR場在對稱和非對稱厚膜模型中(三參數(shù)厚膜解)的局域化性質(zhì)。結(jié)果表明,KR場的KK模式的有效勢為火山勢,故而存在膜上無質(zhì)量的KR場和一些有質(zhì)量的KK共振態(tài)。我們通過相對概率算法來研究對稱厚膜的KK共振態(tài),并首次采用了轉(zhuǎn)移矩陣的算法計算非對稱厚膜模型中的KK共振態(tài)。當(dāng)模型參數(shù)s(s=1單膜、s1雙膜)有限時,共振態(tài)的數(shù)目會隨著膜厚度參數(shù)λ的增加、或耦合參數(shù)p的減小而增加。最后,我們對存在相互作用的u(1)規(guī)范場(也可看作變質(zhì)量的矢量場)在對稱與非對稱Bloch厚膜模型中的局域化及準(zhǔn)局域問題作了深入的研究。將五維時空中的U(1)規(guī)范場分解為一個矢量自由度和兩個標(biāo)量自由度,并得到了Bloch厚膜上無質(zhì)量的U(1)規(guī)范場以及一些有質(zhì)量的KK共振態(tài)。研究發(fā)現(xiàn),兩個標(biāo)量自由度的無質(zhì)量模式之間存在耦合,而有質(zhì)量的KK模式卻是脫耦的,并且KK模式的有效勢為無限深勢阱。因此,我們得到了一個無質(zhì)量的標(biāo)量模式以及兩個系列有質(zhì)量的標(biāo)量模式。
[Abstract]:The theory of the extra-dimensional and film world is of great concern because of its ability to solve the basic problems in physics, such as the problem of specification, the problem of cosmological constant, and so on. In the theory of film world, a very important task is to study the mechanism of various material fields on the membrane in high-dimensional space, so as to realize the reconstruction of the particle physical standard model on the four-dimensional film and provide guidance for future experiments. In addition, the problem of dark matter has become one of the leading topics in the current physics, and in the supersymmetric theory, the gravitational micro-field is the supersymmetric Fermi-type accompanying particle of the gravitational sub, and is considered one of the candidates for dark matter. This paper will focus on the localized properties of the gravitational micro-field and the canonical field (Kalb-Ramond (KR) field and vector field) on the film and the thick film in the five-dimensional film world theory. In this paper, we first review the additional dimension theory and the development of the film world theory, and introduce the KK theory and several main film world theories (including the famous Arkani-Hamed-Dimopoulos-Dvali (ADD) model, the Ra-ndall-Sundram (RS) model, and the scalar tensor film world model). The ADD and RS models are thin-film models, which mainly solve the problem of the specification level, thus the prologue of the film world theory is uncovered. However, the film model is an ideal model to ignore the film thickness. Considering the actual thickness of the film, the theory of thick film and the development of the film world are further promoted. In the thick film theory, the background scalar field is introduced as the material field for constructing the thick film, so that the energy density of the film has a certain distribution along the extra dimension. Since the scalar field of the thick film does not define a specific form, the world solution of the thick film film has diversity. Secondly, we have studied the localization properties of the five-dimensional gravitational micro-field in the film model (RS and the scalar tensor film world model) with S1/ Z2 topological defects in the extra dimension. The results show that (i) for the RS model, there are no quality hand sign modes on the membrane and a series of KK hand sign modes with quality, and the KK hand sign modes with lower energy levels in the physical coordinate are bound to the vicinity of the TeV film; (ii) For the scalar tensor film world model (considering the two solutions), the size of the model parameter value determines the localization property of the non-mass hand sign mode, and the mass spectrum and the local property of the gravitational micro-sub are different for the two solutions, indicating that the two solutions are not physically equivalent. In the third chapter, we introduce a special coupling form f (p (z)) = e (-7-2p) A (z) (p-9/ 2) to study the localization properties of the KR field in the symmetric and asymmetric thick film model (three-parameter thick film solution). The results show that the effective potential of the KK mode in the KR field is the volcanic potential, so there is no quality KR field and some quality KK resonance states on the membrane. In this paper, the KK resonance state of the symmetric thick film is studied by the relative probability algorithm, and the K-K resonance state in the asymmetric thick-film model is calculated for the first time by using the transfer matrix algorithm. When the model parameter s (s = 1 single film, s1 double film) is limited, the number of resonance states increases as the film thickness parameter s increases or the coupling parameter p decreases. In the end, we have studied the local and quasi-local problems in the symmetric and asymmetric Bloch-thick film model for u (1) specification field with interaction (which can also be regarded as the vector field of variable mass). The U (1) specification field in the air at the time of five dimensions is decomposed into a vector degree of freedom and two scalar degrees of freedom, and the non-mass U (1) specification field and some quality KK resonance states on the Bloch thick film are obtained. It has been found that there is a coupling between two scalar-of-freedom-free modes, while the KK mode with the quality is decoupled and the effective potential of the KK mode is the infinite potential well. As a result, we have a quality scalar pattern and two series of quality scalar patterns.
【學(xué)位授予單位】：蘭州大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O572.2
本文編號：2376046
[Abstract]:The theory of the extra-dimensional and film world is of great concern because of its ability to solve the basic problems in physics, such as the problem of specification, the problem of cosmological constant, and so on. In the theory of film world, a very important task is to study the mechanism of various material fields on the membrane in high-dimensional space, so as to realize the reconstruction of the particle physical standard model on the four-dimensional film and provide guidance for future experiments. In addition, the problem of dark matter has become one of the leading topics in the current physics, and in the supersymmetric theory, the gravitational micro-field is the supersymmetric Fermi-type accompanying particle of the gravitational sub, and is considered one of the candidates for dark matter. This paper will focus on the localized properties of the gravitational micro-field and the canonical field (Kalb-Ramond (KR) field and vector field) on the film and the thick film in the five-dimensional film world theory. In this paper, we first review the additional dimension theory and the development of the film world theory, and introduce the KK theory and several main film world theories (including the famous Arkani-Hamed-Dimopoulos-Dvali (ADD) model, the Ra-ndall-Sundram (RS) model, and the scalar tensor film world model). The ADD and RS models are thin-film models, which mainly solve the problem of the specification level, thus the prologue of the film world theory is uncovered. However, the film model is an ideal model to ignore the film thickness. Considering the actual thickness of the film, the theory of thick film and the development of the film world are further promoted. In the thick film theory, the background scalar field is introduced as the material field for constructing the thick film, so that the energy density of the film has a certain distribution along the extra dimension. Since the scalar field of the thick film does not define a specific form, the world solution of the thick film film has diversity. Secondly, we have studied the localization properties of the five-dimensional gravitational micro-field in the film model (RS and the scalar tensor film world model) with S1/ Z2 topological defects in the extra dimension. The results show that (i) for the RS model, there are no quality hand sign modes on the membrane and a series of KK hand sign modes with quality, and the KK hand sign modes with lower energy levels in the physical coordinate are bound to the vicinity of the TeV film; (ii) For the scalar tensor film world model (considering the two solutions), the size of the model parameter value determines the localization property of the non-mass hand sign mode, and the mass spectrum and the local property of the gravitational micro-sub are different for the two solutions, indicating that the two solutions are not physically equivalent. In the third chapter, we introduce a special coupling form f (p (z)) = e (-7-2p) A (z) (p-9/ 2) to study the localization properties of the KR field in the symmetric and asymmetric thick film model (three-parameter thick film solution). The results show that the effective potential of the KK mode in the KR field is the volcanic potential, so there is no quality KR field and some quality KK resonance states on the membrane. In this paper, the KK resonance state of the symmetric thick film is studied by the relative probability algorithm, and the K-K resonance state in the asymmetric thick-film model is calculated for the first time by using the transfer matrix algorithm. When the model parameter s (s = 1 single film, s1 double film) is limited, the number of resonance states increases as the film thickness parameter s increases or the coupling parameter p decreases. In the end, we have studied the local and quasi-local problems in the symmetric and asymmetric Bloch-thick film model for u (1) specification field with interaction (which can also be regarded as the vector field of variable mass). The U (1) specification field in the air at the time of five dimensions is decomposed into a vector degree of freedom and two scalar degrees of freedom, and the non-mass U (1) specification field and some quality KK resonance states on the Bloch thick film are obtained. It has been found that there is a coupling between two scalar-of-freedom-free modes, while the KK mode with the quality is decoupled and the effective potential of the KK mode is the infinite potential well. As a result, we have a quality scalar pattern and two series of quality scalar patterns.
【學(xué)位授予單位】：蘭州大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O572.2
【相似文獻(xiàn)】
相關(guān)博士學(xué)位論文 前1條
1 杜云芝;膜世界中引力微子場和規(guī)范場的局域化[D];蘭州大學(xué);2016年
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