Investigations of the torque anomaly in an annular sector. I. Global calculations, scalar case
Investigations of the torque anomaly in an annular sector. I. Global calculations, scalar case
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环形扇区扭矩异常的研究。
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
K. Kirsten
中科院分区：
文献类型：
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作者：
K. Milton;F. Kheirandish;Prachi Parashar;E. Abalo;S. Fulling;J. D. Bouas;H. Carter;K. Kirsten
为了理解最近发现的力矩异常在量子场论的边界，我们计算Casimir能量和力矩的标量场的Dirichlet边界条件下的定义由两个同轴的圆柱相交的两个平面通过轴的环形扇区。在这个模型中，特别麻烦的发散在圆柱轴上没有出现，但新的发散与弯曲的边界被引入。与体积、表面积、角点和曲率相关的所有发散都通过在圆柱体的轴向或在（欧几里德）时间方向上的点分离来调节;完整的发散结构被隔离，并且提取剩余的有限能量和扭矩。形式上，只有基于轴分裂的调节器产生能量和扭矩之间的预期平衡。由于对数曲率发散，能量对楔角的线性依赖性存在模糊性;如果通过重整化过程去除该角度中的常数项和线性项，则保留预期的扭矩-能量平衡。
In an attempt to understand a recently discovered torque anomaly in quantum field theory with boundaries, we calculate the Casimir energy and torque of a scalar field subject to Dirichlet boundary conditions on an annular sector defined by two coaxial cylinders intercut by two planes through the axis. In this model the particularly troublesome divergence at the cylinder axis does not appear, but new divergences associated with the curved boundaries are introduced. All the divergences associated with the volume, the surface area, the corners, and the curvature are regulated by point separation either in the direction of the axis of the cylinder or in the (Euclidean) time; the full divergence structure is isolated, and the remaining finite energy and torque are extracted. Formally, only the regulator based on axis splitting yields the expected balance between energy and torque. Because of the logarithmic curvature divergences, there is an ambiguity in the linear dependence of the energy on the wedge angle; if the terms constant and linear in this angle are removed by a process of renormalization, the expected torque-energy balance is preserved.