q-deformed bi-local fields

We study the q-deformation of a bi-local, two particle system, bounded by a relativistic harmonic oscillator type of potential from the points of view of both mass spectra and the behavior of scattering amplitudes. In particular, we attempt to formulate the deformation so that P2, the square of the center-of- mass momenta, enters into the deformation parameters of the relative coordinates. As a result, the wave equation of the bi-local system becomes non-linear with respect to P2; then, the propagator of the bi-local system undergoes a significant change whereby its self-energy becomes convergent to second order. (author)