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A didactic and systematic derivation of Noether point symmetries andconserved currents is put forward in special relativistic field theories,without a priori assumptions about the transformation laws. Given theLagrangian density, the invariance condition develops as a set of partialdifferential equations determining the symmetry transformation. The solution isprovided in the case of real scalar, complex scalar, free electromagnetic, andcharged electromagnetic fields. Besides the usual conservation laws, a lesspopular symmetry is analyzed: the symmetry associated with the linearsuperposition of solutions, whenever applicable. The role of gauge invarianceis emphasized. The case of the charged scalar particle under externalelectromagnetic fields is considered, and the accompanying Noether pointsymmetries determined.

Systematic Derivation of Noether Point Symmetries in Special Relativistic Field Theories