论文标题
一般协方差和Weyl异常的有限尺寸效应
Finite Size Effects from General Covariance and Weyl Anomaly
论文作者
论文摘要
通过利用差异不变性，我们将无质量理论的有限尺寸效应与它们的Weyl异常联系起来。我们表明，对有限尺寸效应的普遍贡献是由相关波算子的热核扩展中的某些系数函数确定的。对于限制在$ 4 $维的弯曲时空中的无质量标量，给出了相关系数 - 确认了Moss和Dowker以及Branson和Gilkey的结果。我们将一般结果应用于二维和四维平面空间中有限区域的理论，并确定区域任意保形变形下有效作用的变化。
By exploiting the diffeomorphism invariance we relate the finite size effects of massless theories to their Weyl anomaly. We show that the universal contributions to the finite size effects are determined by certain coefficient functions in the heat kernel expansion of the related wave operators. For massless scalars confined in a $4$-dimensional curved spacetime with boundary the relevant coefficients are given -- confirming the results of Moss and Dowker and also of Branson and Gilkey. We apply the general results to theories on bounded regions in two- and four-dimensional flat space-times and determine the change of the effective action under arbitrary conformal deformations of the regions.
