New symmetries and conservation laws for electromagnetic fields

It is well known that classical conservation laws of energy, momentum, angular momentum and center-of-energy movement of the electromagnetic field are the consequences of the Maxwell equations invariance with respect to Poincare transformations. However, the relativistic invariance does not exhaust all symmetry properties of these equations. A natural question arises whether there exist any other conservation laws for electromagnetic fields different from those above. One could expect a positive answer to this question to be obtained provided that Maxwell equations possess an additional symmetry different from the relativistic and conformal invariances, because the symmetry under the proper conformal transformations does not lead to any new conserved quantities [1]. We will show in this paper that electromagnetic field equations do possess an additional (nongeometric) symmetry with respect to the GL(2)⊗GL(2) group, which gives rise to new conservation laws. 1. It is well known [2] that the maximal symmetry group of Maxwell equations