Quantum Electrodynamics (QED) Driving Longitudinal Scalar Wave (LSW) Descriptions and Their Physics and Mathematical Equations

QED (quantum electrodynamics) is the QFT (quantum field theory) describing the interaction between light and matter. While conventional QED is based on TEM (transverse electromagnetic) waves, there has been increasing interest in the theoretical and experimental exploration of LSW (longitudinal scalar waves) solutions that are often omitted in CED (classical electrodynamics) but may have physical significance in nontrivial vacuum conditions. This paper delves into the theoretical foundation of LSW, their role in QED, and the associated mathematical equations governing their dynamics.