Elimination of Primitive Divergents from Field Theory by Means of Complex Coupling Constants

Abstract

LSZ. iteration theory is extended to accommodate quantum fields coupled by complex constants, while retaining a positive metric and a Hermitian Hamiltonian. Interpolating and particle (~in, out) fields are linked by an operator U(t) which is nonunitary, so that Haag's theorem may be avoided. It is shown that U(t) may be rendered sufficiently well-behaved as t -+ ± 00 to allow development of the iteration series for the T function. For certain combinations of fields the coupling constants and masses can then be chosen so as to eliminate the primitive divergents from the iteration series for any S-matrix element. The theory is illustrated by two models: four spinor plus two scalar fields, and the electromagnetic plus several spinor fields. In the second model not every spinor field corresponds to a stable physical particle, and the LSZ formalism is extended to allow for this.