Photon-Field Interactions: A Relativistic and Quantum Approach

This study explores photon-field interactions within the framework of Quantum Field Theory (QFT) by integrating relativistic Maxwell equations with chaotic systems, offering a novel approach to effective potentials. The dynamics of electric and magnetic fields in the presence of photons are redefined through the introduction of an effective potential that bridges the kinetic energy term in the Hamiltonian operator with a relativistic framework. By formulating fourth-order partial differential equations, the impact of rapid variations and charge density discontinuities on field behavior is analyzed. Boundary conditions are defined using the Lorenz system, where specific parameter constraints yield quasi-stable solutions. This unified framework highlights photon-field coupling, emphasizing stability, nonlinearity, and the interplay of quantum and relativistic effects. The findings reveal the potential of chaotic dynamics to advance field theory, providing new insights into photon-mediated interactions and their implications for complex electromagnetic systems.