Cremona Problems Related to Static Pion‐Nucleon Theory

Abstract

AbstractCertain mathematical aspects of the static pion‐nucleon theory are investigated. We start from the fact that the theory in its uniformized form (cuts transformed away) leads to a system of functional equations for the S‐matrix. The nonlinear mapping involved in the functional equations is a second‐order Cremona transformation. After a summary of the general properties of Cremona transformations, the special transformations are studied which arise in the symmetric scalar and the Chew‐Low theory respectively. The emphasis is on the possibility to separate, by means of a finite‐order Cremona transformation, the functional equations into a set of uncoupled ones. For the symmetric scalar theory, the separation is trivial. For the Chew‐Low theory, a proof of nonseparability is given.