论文标题
在不可穿透的磁管的背景下，带有量子电荷标量物质的诱导真空能量密度具有Neumann边界条件
Induced vacuum energy density of quantum charged scalar matter in the background of an impenetrable magnetic tube with the Neumann boundary condition
论文作者
论文摘要
我们考虑了带有磁通量内部的带电标量材料场的真空极化。该试管对于量子物质是无法穿透的，并且在其表面施加了完美的刚性（Neumann）边界条件。我们为任意尺寸空间和磁通量的任意值的情况下为诱导的真空能量密度撰写表达式。我们对伦敦通量单元和（2+1）二维时空的半数通量值进行数值计算。我们表明，如果物质场的康普顿波长大大超过管子的横向大小，则诱导了带电标量物质场的诱导真空能。我们表明，真空能在管的磁通量值中是周期性的，从而提供了Aharonov-Bohm效应的量子场理论表现。在其厚度的不同值下，诱导的真空能的依赖性在距管中心的距离上的依赖性。将获得的结果与在完美反射（DIRICHLET）边界条件的情况下进行比较。结果表明，在Neumann边界条件的情况下，诱导的真空能密度的值大于Dirichlet边界条件的情况。
We consider vacuum polarization of charged scalar matter field outside the tube with magnetic flux inside. The tube is impenetrable for quantum matter and the perfectly rigid (Neumann) boundary condition is imposed at its surface. We write expressions for induced vacuum energy density for the case of a space of arbitrary dimension and for an arbitrary value of the magnetic flux. We do the numerical computation for the case of half-integer flux value in the London flux units and (2+1)-dimensional space-time. We show that the induced vacuum energy of the charged scalar matter field is induced if the Compton wavelength of the matter field exceeds the transverse size of the tube considerably. We show that vacuum energy is periodic in the value of the magnetic flux of the tube, providing a quantum-field-theoretical manifestation of the Aharonov-Bohm effect. The dependencies of the induced vacuum energy upon the distance from the center of the tube under the different values of its thickness were obtained. Obtained results are compared to the results obtained earlier in the case of the perfectly reflecting (Dirichlet) boundary condition. It is shown that the value of the induced vacuum energy density in the case of the Neumann boundary condition is greater than in the case of the Dirichlet boundary condition.
