COMPLEX HARMONIC-OSCILLATOR BASIS FOR THE RELATIVISTIC 3-BODY PROBLEM

A complex harmonic-oscillator basis is employed for the three-body problem obeying S-3-symmetry. Unlike a real basis it generates an additional quantum number (N-a), in addition to the standard principal quantum number (N), and thus facilitates a more quantitative S-3-classification of the various states than is usually possible. It is shown that certain bilinear forms with definite S-3-symmetry properties, which can be constructed out of the linear harmonic-oscillator operators (alpha,alpha(dagger)) satisfy several uncoupled sets of SO(2, 1) algebras with spectra bounded from below. It is also briefly indicated how this S-3-formalism can be adapted to the core structure of a more general relativistic three-particle system with unequal-mass kinematics through an appropriate choice of internal variables.