Noether analysis of zilch conservation laws and their generalization for the electromagnetic field. I. Use of different formulations of the principle of least action

Conservation laws for the electromagnetic field are obtained in the framework of the Lagrangian approach in terms of field strengths (and not of the potentials) on the basis of the 32-dimensional algebra of invariance of the Maxwell equations and the Noether theorem. The correspondence between symmetry operators and conservation laws is analysed which is determined by various Lagrangians. New sets of conservation laws are found.