Advances in Maxwell’s Equations: Overview, Applications and Relations with Other Foundational Equations of Theoretical Physics

Dear Colleagues, Maxwell’s equations serve as a foundational bridge between classical field theory and the modern quantum and relativistic landscape. This Special Issue, "Advances in Maxwell’s Equations: Overview, Applications and Relations with Other Foundational Equations of Theoretical Physics," seeks to explore this relationship through the lens of rigorous mathematical frameworks. We aim to highlight how modern geometric methods and functional analysis—including the application of Schwartz distribution theory—provide a deeper understanding of electromagnetic phenomena and their interplay with other fundamental wave equations. A central theme of this collection is the formal correspondence between Maxwell’s system and Schrödinger-type equations. We encourage submissions that utilize advanced mathematical tools to investigate existence, uniqueness, and the construction of exact solutions. Whether through the study of underlying symmetries, the application of generalized functions, or the exploration of wave–particle dualities in curved spacetimes, we invite contributors to submit original research that bridges the gap between abstract mathematics and theoretical physics, as well as the gap between classical and quantum physics. By examining Maxwell's theory alongside the foundational equations of quantum and relativistic mechanics, this Special Issue aims to provide a comprehensive overview of the current state of electromagnetic research. Prof. Dr. David Carfì Guest Editor