A Lorentz-Covariant Quaternionic Double Coupled Field Theory from Real Coupled Fields to SU(2), Chirality, and the Dirac Limit

This paper develops a Lorentz-covariant Double Coupled Field (DCF) framework in which a relativistic matter carrier is represented by eight real degrees of freedom organized as two quaternionic coordinates. Starting from coupled real fields, the construction establishes a real Cl(1,3) representation, an internal unit-quaternion symmetry Sp(1) ≅ SU(2), where Sp(1) denotes the group of unit quaternions, together with chirality and controlled Dirac and Schrödinger–Pauli limits. The work investigates the hypothesis that complex structures appearing in standard quantum formulations may represent compact descriptions of underlying coupled real degrees of freedom. The present results establish a consistent classical framework and its limiting correspondence with established relativistic quantum structures; they do not constitute a complete Poincaré-covariant quantum field theory, do not derive the spin–statistics connection, and do not claim experimentally distinguished predictions from the linear Dirac limit. Nonlinear DCF sectors, internal dynamics, and possible two-particle extensions are identified as directions for future investigation. The manuscript distinguishes three theoretical levels: the classical DCF ontology, a conditional full-Sp(1) extension, and a quantized two-particle extension; these levels are kept explicitly separate throughout the analysis.