<strong>Photon-Field Interactions: A Relativistic and Quantum Approach</strong>

This study investigates photon-field interactions by integrating relativistic Maxwell equations with chaotic systems and, provides a novel perspective on effective potentials. This study redefines the dynamics of electric and magnetic fields in the presence of photons by, introducing an effective potential that bridges the kinetic energy term of the Hamiltonian operator with the relativistic framework. By formulating a fourth-order differential equation, the analysis explores the impact of charge density discontinuities and rapid variations on field behavior. Boundary conditions are derived using the Lorenz system, where specific parameter constraints yield quasi- stable solutions. This unified approach sheds light on photon-field coupling, emphasizing its implications for stability, nonlinearity, and the interplay of quantum and relativistic effects. The findings offer a fresh perspective on incorporating chaotic dynamics into field theory, advancing the understanding of photon-mediated interactions in complex systems.