Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-12-03
J.Math.Phys. 35 (1994) 2761-2771
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, no figures, Plain Tex, IASSNS-HEP 93/51
Scientific paper
10.1063/1.530484
In a previous paper, it was shown that a soluble model can be constructed for the description of a decaying system in analogy to the Lee-Friedrichs model of complex quantum theory. It is shown here that this model also provides a soluble scattering theory, and therefore constitutes a model for a decay scattering system. Generalized second resolvent equations are obtained for quaternionic scattering theory. It is shown explicitly for this model, in accordance with a general theorem of Adler, that the scattering matrix is complex subalgebra valued. It is also shown that the method of Adler, using an effective optical potential in the complex sector to describe the effect of the quaternionic interactions, is equivalent to the general method of Green's functions described here.
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