Q-Deformed Bi-Local Fields

TL;DR

This paper explores the q-deformation of a bi-local particle system with a relativistic harmonic oscillator potential, analyzing its mass spectra and scattering amplitudes, and introduces a non-linear wave equation with improved propagator convergence.

Contribution

It formulates a novel q-deformation scheme where the deformation depends on the center of mass momentum squared, leading to a non-linear wave equation and modified propagator behavior.

Findings

Modified mass spectra due to q-deformation

Non-linear wave equation incorporating P^2 dependence

Enhanced convergence of the bi-local system's propagator

Abstract

We study the q-deformation of the bi-local system, 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 particular, we try to formulate the deformation so that $P^2$, the square of center of mass momenta, enters into the deformation parameters of relative coordinates. As a result, the wave equation of the bi-local system becomes non-linear one 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 second order.