Onq-deformation of bi-local system

Abstract

We study a way ofq-deformation of the bi-local system, the two-particle system bounded by a relativistic harmonic-oscillator type of potential, from both points of view of mass spectra and the behavior of scattering amplitudes. In our formulation, the deformation is done so thatP ², the square of center-of-mass momentum, enters into the deformation parameters of relative coordinates. As a result, the wave equation of the bi-local system becomes nonlinear with respect toP ²; then, the propagator of the bi-local system suffers significant change so as to get a convergent self energy to the second order. The study is also made on the covariantq-deformation in four-dimensional spacetime.