A NOTE ON THE SOLUTION OF A SPINOR EQUATION

An equation of spinor algebra, which is specified by two positive integers, M and N, is solved by relating it to the problem of integrating a two-dimensional Hamiltonian homogeneous polynomial system of ordinary differential equations, whose degree is N - 1. The case in which N = 1 reduces to a well-known result of spinor algebra. The case M = N = 4 is of relevance in the study of symmetry operators of Maxwell's equations on a curved space-time. It is also shown, using spinor notation, that the first integral for a general two-dimensional Hamiltonian system of ordinary differential equations (whether polynomial or analytic) is determinable in a purely algebraic manner, i.e., by using no integration.