The core principle established is that classical Abelian gauge theory yields Maxwell electrodynamics through a variational action involving only the vector potential $A_\mu$, where physical observability and well-posed Cauchy problems depend exclusively on the gauge-invariant field strength tensor $F_{\mu\nu}$. The mechanism for resolving the non-uniqueness of time evolution under arbitrary gauge transformations involves imposing constraints such as the Lorenz gauge condition, which reduces redundant degrees of freedom to reveal two physical transverse photon modes. This theoretical framework situates free electrodynamics within quantum field theory by demonstrating how massless boson propagation emerges from wave equations derived after fixing residual gauge invariance.
The core principle established is that classical Abelian gauge theory yields Maxwell electrodynamics through a variational action involving only the vector potential $A_\mu$, where physical observabi…