Momentum-Transfer-Independent Angular Relations and Solutions to the Isospin-Factored Current Algebra

The main purpose of this paper is to construct a general class of solutions to the isospin-factored algebra of form factors at infinite momentum. Lorentz covariance imposes a very restrictive condition on these form factors, which is known as the angular condition. In this paper, we decompose this angular condition into a set of momentum-transfer-independent conditions. To further simplify our problem, we strengthen the angular conditions into three more restrictive and mutually exclusive classes of conditions (called primitive equations). These simplified angular conditions can be solved completely, and lead to three classes of primitive solutions. We find that for each of the primitive solutions there always exists an internal Lorentz group, and that these solutions are related to some very simple infinite-component wave equations. Having established the connection between the solution to the angular conditions and the wave equation, we then turn things around and construct some very general solutions from the coupled wave equations. The fact that these coupled equations represent the most general solutions to the primitive equations suggests that they may already represent the most general solution compatible with the original angular condition. Next, under very mild technical conditions, the solutions to the angular conditions are shown either to be physically trivial or to contain a spacelike ($M^2<0\mathrm{}$) part. The possibility that the spacelike and timelike parts are not coupled by the currents is also discussed.