HOW TO TREAT γ5

In the past two decades, Dyson's formalism of renormalization has been mostly superceded by dimensional regularization, particularly in the treatment of quantum gauge field theories with spontaneous symmetry breaking or those with chiral fermions. In this paper, we shall carry out explicitly Dyson's subtraction program, making it applicable to such field theories. In particular, we show with the example of the Abelian–Higgs theory how to handle amplitudes of chiral fermions. We show that these amplitudes which involve the γ5 matrix can be calculated in an unambiguous and gauge invariant way. This is done by establishing the subtraction conditions for the propagator of a chiral fermion as well as those for the VVV amplitude, when V denotes the vector meson. The renormalized constants are chosen to satisfy the Ward–Takahashi identities. As a demonstration, we calculate the next-lowest order correction of the anomaly in the Abelian–Higgs model and find that it vanishes.