论文标题
Casimir效应在聚合物标量场理论中
Casimir effect in polymer scalar field theory
论文作者
论文摘要
在本文中，我们研究了两个平行导电板的经典几何形状中的Casimir效应，由于存在于背景独立（聚合物）量化方案的最小长度$λ$，因此被距离$ L $隔开。为此，我们将聚合物量化的经典klein-gordon hamiltonian用于限制在板之间的大规模标量场并获得能量谱。该理论的最小长度尺度引入了平行于板平行的平面上的动量的自然截止，板之间的最大数量离散模式。零点能量是通过在模式上求和来计算的，并且假设$λ\ ll l $，我们将其表示为$ 1/ n $的扩展，为$ n = l/λ$ plates之间的点数。在大小的标量质量极限的情况下，获得了Casimir能量的封闭分析表达式。
In this paper, we study the Casimir effect in the classical geometry of two parallel conducting plates, separated by a distance $L$, due to the presence of a minimal length $λ$ arising from a background independent (polymer) quantization scheme. To this end, we polymer-quantize the classical Klein-Gordon Hamiltonian for a massive scalar field confined between the plates and obtain the energy spectrum. The minimal length scale of the theory introduces a natural cutoff for the momenta in the plane parallel to the plates and a maximum number of discrete modes between the plates. The zero-point energy is calculated by summing over the modes, and by assuming $λ\ll L$, we expressed it as an expansion in powers of $1/N$, being $N=L/ λ$ the number of points between the plates. Closed analytical expressions are obtained for the Casimir energy in the cases of small and large scalar mass limits.
