We study generalized heat kernel coefficients, which appear in the trace of the heat kernel with an insertion of a first-order differential operator, by using a path integral representation. These coefficients may be used to study gravitational anomalies, i.e. anomalies in the conservation of the stress tensor. We use the path integral method to compute the coefficients related to the gravitational anomalies of theories in a non-abelian gauge background and flat space of dimensions 2, 4, and 6. In 4 dimensions one does not expect to have genuine gravitational anomalies. However, they may be induced at intermediate stages by regularization schemes that fail to preserve the corresponding symmetry. A case of interest has recently appeared in the study of the trace anomalies of Weyl fermions.

我们通过使用路径积分表示来研究广义热核系数，该系数在热核迹中插入一阶微分算符后出现。这些系数可用于研究重力异常，即应力张量守恒中的异常。我们使用路径积分法来计算与非阿贝尔规范背景中的理论引力异常相关的系数，以及尺寸为2、4和6的平面空间。在4个维度中，一个期望不会出现真正的引力异常。但是，它们可能会在中间阶段通过无法保留相应对称性的正则化方案来诱发。最近对Weyl费米子的痕量异常的研究中出现了一个有趣的案例。