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Relativistic Electrodynamics: Covariant Formulation and Gauge Invariance

The theoretical framework establishes that relativistic electrodynamics is formulated using covariant tensor equations where Maxwell's laws express conservation via field tensors derived from four-vector potentials. A core principle defined is gauge invariance, the property wherein physical electromagnetic fields remain invariant under arbitrary transformations of the potential vector added by a scalar function gradient. This formalism relates classical electromagnetism to relativistic geometry and serves as a foundational mechanism for introducing constraints like Lorenz gauge conditions within quantum field theory.