厚膜中玻色场俘获的新解析解
New Analytical Solutions for Bosonic Field Trapping in Thick Branes
摘要：
本文给出了Randall-Sundrum（RS）模型中引力场、标量场和矢量场局部化的新的解析解，定义了一个光滑的翘曲因子，并在壁面内引入了一个相关函数$f(z)=\exp(3A(z)/2)$（$|z|<d$），导出了一个相关方程，并对背景的连续性和光滑性进行了物理约束，从而得到了一个新的解析解空间。我们解决这个相关的方程解析抛物和Pöschl-Teller势和分析这些领域的共振谱。通过使用边界条件，我们能够表明，对于任何这些解决方案，密度概率找到一个大规模的模式在膜具有普遍的行为，小的质量值由$|ψ_m(0)|^2=β_1m+β_3m^3+β_L m^3\log(m)+\cdots$。因此，例如对牛顿定律的首阶修正的形式是通用的，并且不依赖于所使用的势。最后，我们还讨论了为什么复杂的出现时，我们试图使用的方法来找到费米子的情况下的解析解。
英文摘要：
New analytical solutions for gravity, scalar and vector field localization in Randall-Sundrum(RS) models are found. A smooth version of the warp factor with an associated function $f(z)=\exp(3A(z)/2)$ inside the walls ($|z|<d$) is defined, leading to an associated equation and physical constraints on the continuity and smoothness of the background resulting in a new space of analytical solutions. We solve this associated equation analytically for the parabolic and Pöschl-Teller potentials and analyze the spectrum of resonances for these fields. By using the boundary conditions we are able to show that, for any of these solutions, the density probability for finding a massive mode in the membrane has a universal behavior for small values of mass given by $|ψ_m(0)|^2=β_1m+β_3m^3+β_L m^3\log(m)+\cdots$. As a consequence, the form of the leading order correction, for example, to the Newton's law is general and does not depend on the potential used. At the end we also discuss why complications arises when we try to use the method to find analytical solutions to the fermion case.
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