q-Deformed Bi-Local Fields II

TL;DR

This paper explores a novel q-deformation of the bi-local system, analyzing its effects on mass spectra and scattering amplitudes, leading to nonlinear wave equations and improved propagator convergence.

Contribution

It introduces a new q-deformation approach where the deformation depends on the center of mass momentum, resulting in nonlinear wave equations and modified propagators.

Findings

Wave equation becomes nonlinear in P^2

Propagator shows significant change for convergence

Covariant q-deformation analyzed in 4D spacetime

Abstract

We study a way of $q$-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 that $P^2$, 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 to $P^2$; 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 covariant $q$-deformation in four dimensional spacetime.