任意规范场中四维有质量Dirac传播子和行列式的手征性质
Some chirality-related properties of the 4-D massive Dirac propagator and determinant in an arbitrary gauge field
摘要：
对于任意规范场背景下的四维有质量Dirac场，我们证明了Dirac传播子和泛函行列式完全由二阶Dirac算子的一个手征扇区的相应量的知识决定.这推广了以前已知的（反）自对偶背景规范场中的相关陈述。来自两个手征性扇区的（重正化）函数决定簇的对数仅相差一项，反映了积分手征异常。
英文摘要：
For a 4-D massive Dirac field in the background of arbitrary gauge fields, we show that the Dirac propagator and functional determinant are completely determined by knowledge of the corresponding quantities for just one of the chirality sectors of the second-order Dirac operator. This generalizes the related, previously known, statements in (anti-)self-dual background gauge fields. The logarithms of the (renormalized) functional determinants from the two chirality sectors are shown to be different only by a term reflecting the integrated chiral anomaly.
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