Tsui-Complex Quantum Field Theory:A Structural Reformulation of Fields, Gauge Interactions, and Vacuum Dynamics

Tsui-Complex Quantum Field Theory (TC-QFT) is introduced as a structural reformulation of quantum fields based on the algebra of Tsui-Complex numbers, a two-layer extension of the complex field equipped with two multiplicative structures. This framework naturally encodes discrete–continuous duality, particle–wave duality, and closed–open system behavior within a unified algebraic and geometric structure. The theory is motivated by the OS model, whose higher-dimensional parameter space projects onto the two-layer Tsui-Complex structure. We construct Tsui-Complex fields, gauge interactions, vacuum structure, spontaneous symmetry breaking, and the Higgs mechanism, demonstrating that TC-QFT yields new physical predictions including multi-layer gauge bosons, two-mode Higgs excitations, and modified vacuum dynamics. This work establishes TC-QFT as a coherent and mathematically grounded extension of conventional quantum field theory.