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For a 4-D massive Dirac field in the background of arbitrary gauge fields, weshow that the Dirac propagator and functional determinant are completelydetermined by knowledge of the corresponding quantities for just one of thechirality sectors of the second-order Dirac operator. This generalizes therelated, previously known, statements in (anti-)self-dual background gaugefields. The logarithms of the (renormalized) functional determinants from thetwo chirality sectors are shown to be different only by a term reflecting theintegrated chiral anomaly.

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