膜世界中引力微子场和规范场的局域化
发布时间：2018-12-13 06:14
【摘要】：额外维与膜世界理论由于能够解决物理学中的基本难题,如规范层次问题、宇宙学常数问题等,因而备受关注。在膜世界理论中,一个非常重要的课题就是研究高维时空中的各种物质场局域在膜上的机制,从而实现四维膜上粒子物理标准模型的重构,并为未来的实验提供指导。此外,暗物质问题已成为当前物理学的前沿课题之一,而在超对称理论中引力微子场是引力子的超对称费米型伴随粒子,被认为是暗物质的候选者之一。本论文将重点研究五维膜世界理论中引力微子场和规范场(Kalb-Ramond(KR)场和矢量场)在薄膜及厚膜上的局域化性质。本论文中,我们首先回顾额外维理论以及膜世界理论的发展历程,并介绍了KK理论和几种主要的膜世界理论(包括著名的Arkani-Hamed-Dimopoulos-Dvali(ADD)模型、Ra-ndall-Sundram(RS)模型以及标量张量膜世界模型)。其中ADD和RS模型都是薄膜模型,主要解决规范层次问题,从而揭开了膜世界理论的序幕。然而,薄膜模型是一种忽略膜厚度的理想模型。考虑现实的有厚度的膜进一步促使了厚膜理论的提出和膜世界的发展。在厚膜理论中,通过引入背景标量场来作为构造厚膜的物质场,使得膜的能量密度沿额外维有了一定的分布。由于构建厚膜的标量场没有限定具体的形式,从而厚膜膜世界解具有多样性。其次,我们研究了五维有质量的引力微子场在额外维具有S1/Z2拓扑缺陷的薄膜模型(RS和标量张量膜世界模型)中的局域化性质。研究表明,(i)对于RS模型,存在膜上无质量的手征模式以及一系列有质量的Kaluza-Klein(KK)手征束缚态,且在物理坐标下一些较低能级的KK手征模式均束缚在TeV膜附近；(ii)对于标量张量膜世界模型(考虑两种解),模型参数λ的大小决定着无质量手征模式的局域化性质,且引力微子的质量谱和局域化性质对这两种解是不同,表明了这两种解在物理上是不等价的。接着,第三章中我们通过引入了一种特殊耦合形式f(φ(z))=e(-7-2p)A(z)(p-9/2)来研究KR场在对称和非对称厚膜模型中(三参数厚膜解)的局域化性质。结果表明,KR场的KK模式的有效势为火山势,故而存在膜上无质量的KR场和一些有质量的KK共振态。我们通过相对概率算法来研究对称厚膜的KK共振态,并首次采用了转移矩阵的算法计算非对称厚膜模型中的KK共振态。当模型参数s(s=1单膜、s1双膜)有限时,共振态的数目会随着膜厚度参数λ的增加、或耦合参数p的减小而增加。最后,我们对存在相互作用的u(1)规范场(也可看作变质量的矢量场)在对称与非对称Bloch厚膜模型中的局域化及准局域问题作了深入的研究。将五维时空中的U(1)规范场分解为一个矢量自由度和两个标量自由度,并得到了Bloch厚膜上无质量的U(1)规范场以及一些有质量的KK共振态。研究发现,两个标量自由度的无质量模式之间存在耦合,而有质量的KK模式却是脱耦的,并且KK模式的有效势为无限深势阱。因此,我们得到了一个无质量的标量模式以及两个系列有质量的标量模式。
[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.
【学位授予单位】：兰州大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O572.2
本文编号：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.
【学位授予单位】：兰州大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O572.2
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1 杜云芝;膜世界中引力微子场和规范场的局域化[D];兰州大学;2016年
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