Transverse Ward-Takahashi Identity, Anomaly and Schwinger-Dyson Equation

Details Transverse Ward-Takahashi Identity, Anomaly and Schwinger-Dyson Equation Transverse Ward-Takahashi Identity, Anomaly and Schwinger-Dyson Equation

1996-08-15

arxiv.org/abs/hep-th/9608100v1

Int.J.Mod.Phys.A12:5651-5686,1997

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, latex, no figures

Scientific paper

10.1142/S0217751X97002978

Based on the path integral formalism, we rederive and extend the transverse Ward-Takahashi identities (which were first derived by Yasushi Takahashi) for the vector and the axial vector currents and simultaneously discuss the possible anomaly for them. Subsequently, we propose a new scheme for writing down and solving the Schwinger-Dyson equation in which the the transverse Ward-Takahashi identity together with the usual (longitudinal) Ward-Takahashi identity are applied to specify the fermion-boson vertex function. Especially, in two dimensional Abelian gauge theory, we show that this scheme leads to the exact and closed Schwinger-Dyson equation for the fermion propagator in the chiral limit (when the bare fermion mass is zero) and that the Schwinger-Dyson equation can be exactly solved.

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