HOW TO TREAT GAMMA(5)

In the past two decades, Dyson's formalism of renormalization has been mostly superceded by dimensional regularization, particularly in the treatment of quantum gauge field theories with spontaneous symmetry br eaking or those with chiral fermions. In this paper, we shall carry ou t explicitly Dyson's subtraction program, making it applicable to such field theories. In particular, we show with the example of the Abelia n-Higgs theory how to handle amplitudes of chiral fermions. We show th at these amplitudes which involve the gamma 5 matrix can be calculated in an unambiguous and gauge invariant way. This is done by establishi ng the subtraction conditions for the propagator of a chiral fermion a s well as those for the VVV amplitude, where V denotes the vector meso n. The renormalized constants are chosen to satisfy the Ward-Takahashi identities. As a demonstration, we calculate the next-lowest order co rrection of the anomaly in the Abelian-Higgs model and find that it va nishes.