Structural Algebraic Quantum Field Theory: Particles with Structure

Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the nucleons, which contain quarks and gluons. We introduce a structure-inclusive algebraic formulation of quantum field theory that could handle such particles and in which orthogonal polynomials play a central role. For simplicity, we consider non-elementary scalar particles in 3 + 1 Minkowski space-time and, in an appendix, we treat spinors having structure but in 1 + 1 space-time. We show how scattering calculations are done in this theory for an illustrative example with nonlinear coupling. The aim of this short expose is to motivate further studies and research using this approach.