This study investigates photon-field interactions within the framework of Quantum Field Theory (QFT) by integrating relativistic Maxwell equations with chaotic dynamics, presenting a novel approach to effective potentials. The behavior of electric and magnetic fields in the presence of photons is redefined through an effective potential that connects the kinetic energy term in the Hamiltonian operator to a relativistic framework. By employing fourth-order partial differential equations, the effects of rapid field variations and charge density discontinuities are systematically analyzed. Boundary conditions are established using the Lorenz system, with specific parameter constraints yielding quasi-stable solutions. This unified framework underscores the role of photon-field coupling, highlighting stability, nonlinearity, and the interplay between quantum and relativistic effects. The findings demonstrate the potential of chaotic dynamics to advance field theory, offering new perspectives on photon-mediated interactions and their applications in complex electromagnetic systems.
