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Australian Journal of Physics Australian Journal of Physics Society
A journal for the publication of original research in all branches of physics
RESEARCH ARTICLE

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

AF Nicholson

Australian Journal of Physics 26(6) 703 - 724
Published: 1973

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.

https://doi.org/10.1071/PH730703

© CSIRO 1973

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