Numerical Calculation of the Masses of Light Mesons using the Time-Dependent Dirac Equation with SU(3)-color interactions

This project aims to calculate the masses of light mesons as the bound states of quarks and antiquarks under strong interactions. The 8 gluon gauge fields are calculated using self-coupled equations with non-Abelian terms from the SU(3)-color interactions. The quark field evolves via the Dirac equation coupled to the gauge fields produced by the antiquark and vice versa. All of these are calculated on a numerical scheme with one spatial dimension and a time-step small enough to ensure stability. A 12-dimensional spinor is used to incorporate the 3 color quark fields for the quark into a single object for calculations; the same is done for the antiquark as well. The physical mass of the meson is determined by computing expectation values for the mass operator on symmetric and antisymmetric states. Physical states are identified as the time-asymptotic states of the numerically evolved system. The initial momentum dependence is removed via a statistical renormalization scheme.