Complex Spacetime Extensions in Quantum Electrodynamics: Mass Generation, Cross-Dimensional Stress-Energy Tensors, and Topological Vortices in C⁶

This paper extends Quantum Electrodynamics into a 6D complex manifold, exploring how phase entanglement and extra dimensions generate mass and spin. Mathematical Framework Extends momentum into 6-component vector in complex space with signature ηMN. Uses Clifford algebra with 6×6 Γ matrices built from Dirac and Pauli matrices. Forms a 6×6 Dirac equation coupling fields and fermions in extended space. Extended Fields and Mass Constructs generalized Maxwell tensor with both standard and dual phase fields. Includes scalar phase potential Φ linking fields. Derives mass from imaginary dimensional vorticity, related to phase entanglement angle θ. At θ → π/2, effective velocity drops, trapping energy as rest mass. Stress-Energy and Cross-Dimensional Coupling Introduces a 6×6 stress-energy tensor reflecting real and imaginary pressure exchange. Shows continuity equations coupling real radiation into complex internal pressures. Spin, Topology, and Quantization Expresses fermion spin via integrated vorticity in imaginary dimensions. Defines topological invariants like winding number and Chern-Simons form. Topology ensures stability of localized quantum foam, linking charge quantization with topological invariants. In this model framework mass and spin emerge from extra-dimensional phase structures, stabilizing virtual fields and linking topology to fundamental properties. Thus inertia!