Photon-Field Interactions: A Relativistic and Quantum Approach

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