论文标题
单数背景对Zeta功能的影响的新示例
A New Example of the Effects of a Singular Background on the Zeta Function
论文作者
论文摘要
为了激励我们的讨论，我们考虑了一个1+1维标量场与静态库仑型背景相互作用，以便在单个坐标r上给出量子波动的频谱，其二阶差速器具有与单数系数成比例的单数系数。我们发现该操作员的光谱函数提出了一种有趣的行为：Zeta函数在复杂平面中具有多个极；因此，适当时间的对数出现在热跟踪膨胀中。结果，ZETA函数不能提供有效动作的有限正规化。这项工作扩展了先前在圆锥形奇点的情况下得出的类似结果。
To motivate our discussion, we consider a 1+1 dimensional scalar field interacting with a static Coulomb-type background, so that the spectrum of quantum fluctuations is given by a second-order differential operator on a single coordinate r with a singular coefficient proportional to 1/r. We find that the spectral functions of this operator present an interesting behavior: the zeta function has multiple poles in the complex plane; accordingly, logarithms of the proper time appear in the heat-trace expansion. As a consequence, the zeta function does not provide a finite regularization of the effective action. This work extends similar results previously derived in the context of conical singularities.
