Unification of gravity and the harmonic oscillator on a quantum black hole horizon II: Perturbative particle scattering and Feynman amplitudes

Abstract

In Article I, a harmonic-oscillator model of a universe of n quarks is infinitesimally modified to eliminate the background reference frame. As a result, quark trajectories exhibit the unification of gravity and the harmonic oscillator near the horizon of a quantum black hole, a region that is approximately flat in space-time. Constituent quarks are confined to composite particles by cluster decomposition rather than a binding force. Here, the composite-particles are input for a perturbation model of particle-exchange interactions. As in Article I, the Hamiltonian cannot be expressed as H=H0+HI where H0 generates the unperturbed equations of motion. In the present article, H0 annihilates the initial state. Quark substructures yield exchange particles of various masses and angular momenta and thus a natural unification of forces. The background-frame elimination in the fundamental model implies causality and unitarity in the effective model. Feynman propagators are derived and first-order scattering amplitudes are calculated for elastic and inelastic scattering.