Abstract
This thesis investigates and compares the gauge invariance of the leptonic gauge field and the electromagnetic gauge field, where the electric charge corresponds to the leptonic charge. We examine the abelian U₁ gauge symmetry of electrodynamics. Then we apply the same study on lepton dynamics using a new U₁ℓ gauge transformation. Our work involves finding Maxwell equations in electrodynamics and Leon equations for the lepton case. This research also investigates covariant Green function for both electron and lepton dynamics. Our findings might be related to several cosmological implications. Keywords: abelian gauge symmetry, lepton dynamics, particle-cosmology.