标题： 从狄拉克算子行列式得到的广义杨-米尔斯作用 显示英文标题

标题： Generalized Yang-Mills actions from Dirac operator determinants

摘要： 我们考虑在四维平坦欧几里得空间上耦合到外部矢量和轴矢Yang-Mills场的狄拉克费米子的量子有效作用量，即由广义Yang-Mills场扭曲的平坦R^4上的狄拉克算子的（正则化）行列式的对数。根据物理学中的常识，纯矢量情况下此有效作用量的对数发散部分与Yang-Mills作用量成比例。我们给出了一个显式计算，证明了这一事实，并将其推广到手征情况。我们使用了一种高效的量子有效作用量计算方法，该方法基于伪微分算子的计算规则，并能将狄拉克算子的对数展开为降序尺度维度的局部和准规范不变多项式。 显示英文摘要

摘要： We consider the quantum effective action of Dirac fermions on four dimensional flat Euclidean space coupled to external vector- and axial Yang-Mills fields, i.e., the logarithm of the (regularized) determinant of a Dirac operator on flat R^4 twisted by generalized Yang-Mills fields. According to physics folklore, the logarithmic divergent part of this effective action in the pure vector case is proportional to the Yang-Mills action. We present an explicit computation proving this fact, generalized to the chiral case. We use an efficient computation method for quantum effective actions which is based on calculation rules for pseudo-differential operators and which yields an expansion of the logarithm of Dirac operators in local and quasi-gauge invariant polynomials of decreasing scaling dimension.