arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0903.3765hep-th
收藏

额外维时空中有质量标量场的有限温度Casimir效应

Finite temperature Casimir effect for massive scalar field in spacetime with extra dimensions

L. P. Teo

备注：
28 pages, 4 figures
发表信息：
JHEP 0906:076,2009
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

本文计算了具有一般曲率耦合的大质量标量场在任意截面封闭圆柱壁上的Dirichlet或Neumann边界条件下的有限温度Casimir能量，该圆柱位于形式为$M^{d_1+1}\times \mathcal{N}^n$的背景时空中，其中$M^{d_1+1}$是$(d_1+1)$维Minkowski时空，$\mathcal{N}^n$是$n$维内部流形.卡西米尔能量是正规化的标准，它应该消失在无限质量极限。本文导出了作用在封闭圆柱内自由运动的活塞上的Casimir力，并证明了它与正则化过程无关。假设活塞将圆柱分成无限长的两个腔室，我们得到作用在圆柱中两平行板上的卡西米尔力。结果表明，如果两个板假设Dirichlet或Neumann边界条件，卡西米尔力的强度降低的质量增加。在一定条件下，从无质量到有质量的转变会使力的性质从长程转变为短程。Casimir力的其他性质，如它的符号，它在低温和高温下的行为，以及它在小和大的板分离的行为，被发现是类似于无质量的情况。导出了Casimir力在不同极限下的显式精确公式和渐近行为。本文还导出了一个板在Dirichlet边界条件下和一个板在Neumann边界条件下的Casimir力，并证明了Casimir力是相互排斥的。

英文摘要：

We compute the finite temperature Casimir energy for massive scalar field with general curvature coupling subject to Dirichlet or Neumann boundary conditions on the walls of a closed cylinder with arbitrary cross section, located in a background spacetime of the form $M^{d_1+1}\times \mathcal{N}^n$, where $M^{d_1+1}$ is the $(d_1+1)$-dimensional Minkowski spacetime and $\mathcal{N}^n$ is an $n$-dimensional internal manifold. The Casimir energy is regularized using the criteria that it should vanish in the infinite mass limit. The Casimir force acting on a piston moving freely inside the closed cylinder is derived and it is shown that it is independent of the regularization procedure. By letting one of the chambers of the cylinder divided by the piston to be infinitely long, we obtain the Casimir force acting on two parallel plates embedded in the cylinder. It is shown that if both the plates assume Dirichlet or Neumann boundary conditions, the strength of the Casimir force is reduced by the increase in mass. Under certain conditions, the passage from massless to massive will change the nature of the force from long range to short range. Other properties of the Casimir force such as its sign, its behavior at low and high temperature, and its behavior at small and large plate separations, are found to be similar to the massless case. Explicit exact formulas and asymptotic behaviors of the Casimir force at different limits are derived. The Casimir force when one plate assumes Dirichlet boundary condition and one plate assumes Neumann boundary condition is also derived and shown to be repulsive.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑