Introduction of internal coordinates into the infinite-component Majorana equation

Abstract

Given an infinite-component wave equation describing the global quantum numbers of a system one can introduce various internal dynamical coordinates such that ‘constituents’ will appear to move in an oscillator or in a Kepler potential, or, in principle, in other potentials. This is explicitly shown for the Majorana equation. The space-like solutions of the Majorana equations correspond to the scattering state-solutions in terms of the constituent ‘particles’. Light-like solutions and a generalized second-order Majorana equation are also treated in a similar way. Relation to Dirac’s new wave equation without negative energy solutions is discussed.