Some chirality-related properties of the 4-D massive Dirac propagator and determinant in an arbitrary gauge field

Details Some chirality-related properties of the 4-D massive Dirac propagator and determinant in an arbitrary gauge field Some chirality-related properties of the 4-D massive Dirac propagator and determinant in an arbitrary gauge field

2010-07-27

arxiv.org/abs/1007.4616v2

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, latex

Scientific paper

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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