Moduli Stabilization in Warped Compactifications at One Loop

We review the moduli stabilization mechanism found in Garriga et al. (Garriga, J., Pujolas, O., and Tanaka, T. (2000). Preprint hep-th/0111277.) for a class of five-dimensional warped brane-world scenarios. Specifically, we consider solutions with a power-law warp factor and a bulk dilaton with logarithmic profile in terms of the proper distance in the extra dimension. This includes the Heterotic M-theory brane-world of Lukas et al. (Lukas, A., Ovrut, B. A., Stelle, K. S., and Waldram, D. (1999). Physical Review D 59, 086001.) and Khoury et al. (Khoury, J., Ovrut, B. A., Steinhardt, P. J., and Turok, N. (2001). Preprint hep-th/0103239.) and the Randall–Sundrum (RS) model as a limiting case. In general, there are two moduli fields y _±, corresponding to the positions of two branes. Classically, the moduli are massless due to a scaling symmetry of the action. However, in the absence of supersymmetry, they develop an effective potential at one loop. Local terms proportional to some powers of the local curvature scale at the location of the corresponding brane are needed in order to remove the divergences in the effective potential. Such terms break the scaling symmetry and therefore act as stabilizers for the moduli. Moreover, for q 10, the observed hierarchy can be naturally generated by this potential, and the lightest modulus mass is of order m _– TeV.     

Spatial Warped Gaussian Processes: Estimation and Efficient Field Reconstruction

A class of models for non-Gaussian spatial random fields is explored for spatial field reconstruction in environmental and sensor network monitoring. The family of models explored utilises a class of transformation functions known as Tukey g-and-h transformations to create a family of warped spatial Gaussian process models which can support various desirable features such as flexible marginal distributions, which can be skewed, leptokurtic and/or heavy-tailed. The resulting model is widely applicable in a range of spatial field reconstruction applications. To utilise the model in applications in practice, it is important to carefully characterise the statistical properties of the Tukey g-and-h random fields. In this work, we study both the properties of the resulting warped Gaussian processes as well as using the characterising statistical properties of the warped processes to obtain flexible spatial field reconstructions. In this regard we derive five different estimators for various important quantities often considered in spatial field reconstruction problems. These include the multi-point Minimum Mean Squared Error (MMSE) estimators, the multi-point Maximum A-Posteriori (MAP) estimators, an efficient class of multi-point linear estimators based on the Spatial-Best Linear Unbiased (S-BLUE) estimators, and two multi-point threshold exceedance based estimators, namely the Spatial Regional and Level Exceedance estimators. Simulation results and real data examples show the benefits of using the Tukey g-and-h transformation as opposed to standard Gaussian spatial random fields in a real data application for environmental monitoring.     

New Realizations of the Maximal Satake Compactifications of Riemannian Symmetric Spaces of Noncompact Type

We give new realizations of the maximal Satake compactifications of Riemannian symmetric spaces of noncompact type as orbit closures inside Grassmannians and orthogonal groups. Our constructions are partially motivated by Poisson geometry.     

Phantom-Like Effects on Warped DGP Brane

We study phantom-like effect on the DGP brane embedded in a five-dimensional AdS bulk. We show that this effect can be realized without phantom matter on this warped DGP brahe. We investigate the role played by the bulk cosmological constant on the phantom-like effect on the brane and we show that it tends to reduce this effect. Also, warped compactification of the bulk manifold increases the values of the effective and total equation of state parameters of the model relative to the case with Minkowski bulk. We extend our study to the ease that induced curvature on the brahe is modified in the spirit of the f（R）-gravity.     

Boson Fields on the Circle as Generalized Wightman Fields

We define an operator-valued distribution on the circle with the expected properties (correlation functions, Hermiticity, etc.) of the logarithmic boson field in the cylinder compact picture. This is done starting from the known Krein space realization of the right and left movers on the light cone and considering its relation with the U(1)-current algebra. The relevance of this construction fortwo-dimensional conformal quantum field theory is discussed.     

Quantum Stabilization of Moduli in a Slice of AdS6 Compactified on S 1

We review the effective potential due to massive bulk scalar fields in higher-dimensional warped brane models found in Flachi et al. (Quantum stabilization of moduli in higher dimensional brane models, arXiv:hep-th/0301, 2003) specializing it to a slice of AdS₆ compactified on the circle. This model contains two moduli that parametrize the interbrane distance and the size of S ¹, or equivalently the positions of the two branes. Their values determine the Planck/EW hierarchy, in a combination of large volume and redshift effects. It is found that the observed hierarchy is compatible with both moduli stabilized by the Casimir forces without fine-tuning (except for the one needed to match the cosmological constant). This contrasts with the Randall—Sundrum model, where gauge fields in the bulk are needed.     

Classes on Compactifications of the Moduli Space of Curves Through Solutions to the Quantum Master Equation

In this paper we describe a construction which produces classes in compactifications of the moduli space of curves. This construction extends a construction of Kontsevich which produces classes in the open moduli space from the initial data of a cyclic A _∞-algebra. The initial data for our construction are what we call a ‘quantum A _∞-algebra’, which arises as a type of deformation of a cyclic A _∞-algebra. The deformation theory for these structures is described explicitly. We construct a family of examples of quantum A _∞-algebras which extend a family of cyclic A _∞-algebras, introduced by Kontsevich, which are known to produce all the kappa classes using his construction.      

Bounded Bose Fields

Examples for bounded Bose fields in two dimensions are presented.     

Barrier Li Quantum Dots in Magnetic Fields

The methods for the few-body system are introduced to investigate the states of the barrier Li quantumdots (QDs) in an arbitrary strength of magnetic field. The configuration, which consists of a positive ion located on thez-axis at a distance d from the two-dimensional QD plane (the x-y plane) and three electrons in the dot plane boundby the positive ion, is called a barrier Li center. The system, which consists of three electrons in the dot plane bound bythe ion, is called a barrier Li QD. The dependence of energy of the state of the barrier Li QD on an external magneticfield B and the distance d is obtained. The angular momentum L of the ground states is found to jump not only withthe variation of B but also with d.     

QED中相互作用场的量子化

提出在QED中利用自由场的量子化条件和场方程,可以全面解决独立和非独立的相互作用场中￠(x),Aμ(x)的量子化问题.证明了:(1)当外规范场(x)≠0时,￠(x)与Aμ(x)相互独立,它与常规的场量子化方法一致.(2)当(x)=0时,￠(x)与Aμ(x)不再相互独立,常规的量子化方法不再适用,而本文提出的方法继续有效.并以1+1维QED作为实例.     

Evolution of Two Non-identical Two-Level Atoms in Two-Mode Cavity Fields

In this paper, we investigate the evolution of two non-identical two-level atoms in two-mode cavity fields. We demonstrate the death and rebirth effect of entanglement for two non-identical two-level atoms under some initial conditions. It is also exemplified that entangled states of two nonidentical two-level atoms can be generated by entangled two-mode cavity fields. This research can be considered as a first step to further investigate the problem of manipulating two nonidentical two-level atoms in two-mode cavity fields.     

Barrier Li Quantum Dots in Magnetic Fields

The methods for the few-body system are introduced to investigate the states of the barrier Li quantum dots (QDs) in an arbitrary strength of magnetic field. The configuration, which consists of a positive ion located on the z-axis at a distaneed from the two-dimensional QD plane (the x-y plane) and three electrons in the dot plane bound by the positive ion, is called a barrier Li center. The system, which consists of three electrons in the dot plane bound by the ion,is called a barrier Li QD. The dependence of energy of the state of the barrier Li QD on an external magnetic field B and the distance d is obtained. The angular momentum L of the ground states is found to jump not only with the variation orB but also with d.     

强电,磁场中的原子

简要地叙述了强电场和强磁场中的原子物理问题的研究进展，着重介绍了原子电场电离的实验结果和理论分析，对称性对磁场中原子行为的影响，以及与经典混沌和量子谱相关的共振现象。     

Lie Bracket of Vector Fields in Noncommutative Geometry

The aim of this paper is to avoid some difficulties, related with the Lie bracket, in the definition of vector fields in a noncommutative setting, as they were defined by Woronowicz, Schmüdgen-Schüler and Aschieri-Schupp. We extend the definition of vector fields to consider them as derivations of the algebra, through Cartan pairs introduced by Borowiec. Then, using translations, we introduce the invariant vector fields. Finally, the definition of Lie bracket realized by Dubois-Violette, considering elements in the center of the algebra, is also extended to these invariant vector fields.     

紧致空间中辐射场的统计性质

通过对有限紧致空间中辐射场的研究来讨论腔中的原子-辐射场耦合系统. 利用T(1)×SO(4)群的表示, 给出了辐射场的单粒子波函数以及相应的色散关系. 由此详细讨论了紧致空间中辐射场的玻色-爱因斯坦统计. 发现其性质与空间的几何性质(曲率半径)有显著的依赖关系, 并表现与通常黑体辐射系统的显著差异.     

On a Class of Bounded Quantum Bose Fields

Local quantum fields in 1+1 dimensions can have bounded field operators. The class of such fields which in addition obey Huygens' principle (time-like commutativity) and conformal covariance, is completely determined. The result confirms and qualifies a conjecture by K. Baumann.     

Spin 1 Fields in Riemann-Cartan Space-Times via Duffin-Kemmer-Petiau Theory

We consider massive spin 1 fields, in Riemann-Cartan space-times, described by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling between the spin 1 field and the space-time torsion which breaks the usual equivalence with the Proca theory, but that such equivalence is preserved in the context of the Teleparallel Equivalent of General Relativity.