Quantum Electrodynamics of Massive Bosons

This chapter presents a novel theoretical framework that extends quantum electrodynamics to incorporate massive bosons using a quaternionic formalism. By modifying Maxwell’s equations to include a mass term, the study reveals that massive bosons exhibit unique electromagnetic properties: They can sustain a nonzero electric field even when the magnetic field vanishes under suitable gauge transformations. Unlike traditional electrodynamics, which strictly follows the Lorenz gauge condition, this formulation highlights the essential role of boson mass in defining quantum energy and momentum densities. It naturally leads to field equations that satisfy the Klein-Gordon equation and demonstrates a deep equivalence between particle and wave momentum, reinforcing wave-particle duality. The framework predicts novel effects, such as classical Hall conductivity without an external magnetic field and a quantized Hall effect in two-dimensional electron gases (2DEGs). It suggests that phenomena like quantum inductance, critical currents, and quantized capacitance can be directly linked to the mass and spin of bosons. Additionally, the theory introduces gauge-spin transformations that couple spin and helicity densities to the boson’s mass, offering new perspectives on energy-momentum conservation in electromagnetic systems. The model aligns with the established theories, including Wilczek’s axion electrodynamics and the Proca formulation, while opening new experimental possibilities in condensed matter physics, particularly in the study of topological insulators and low-dimensional systems. Overall, this comprehensive framework bridges classical and quantum electrodynamics, providing a unified description of massive boson behavior and a foundation for future theoretical and experimental exploration in modern quantum field theory.