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

TL;DR

This paper develops a perturbative quantum model unifying gravity and harmonic oscillators near a black hole horizon, deriving Feynman amplitudes for particle scattering with novel quark substructure insights.

Contribution

It introduces a new perturbation framework where the Hamiltonian annihilates the initial state, unifying forces through quark substructures and deriving Feynman propagators in this context.

Findings

Derived Feynman propagators for the model

Calculated first-order scattering amplitudes

Unified gravity and harmonic oscillator interactions

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.