Modeling the ground state baryon octet using a generalization of the Lagrange triangle solution

The baryon octet is modeled using relativistic and nonrelativistic Hamiltonians with interquark confining potentials. Using the works of Crater, a nonrelativistic three-body Hamiltonian is obtained where the corresponding eigenvalue equation will be shown to be separable and can be treated as three two-body like systems. Next, using relativistic constraint dynamics, our eigenvalue equation is treated relativistically following the works of Sazdjian and Yang. Using the free-mass-shell Hamiltonian constraints, Yang gives us an effective energy and reduced mass of relative motion for two particle systems which we expand to a three body case. With the help of work done by Sazdjian, we get a generalized 3-body eigenvalue equation in which the energy and reduced masses of effective particles of relative motion are expanded to obtain a form for the eigenvalue equation that can be solved analytically. Because we are dealing with only part of the entire baryon spectrum in which the particles are of the same spin and baryon number, attention will be focused upon confining forces and the development of potentials that are independent of spin and the relative momenta of the fermions. v