Lagrange and Noether analysis of polarization laws of conservation for electromagnetic field

Both well-known Bessel-Hagen conservation laws and conservation laws of polarized character are derived for electromagnetic field in the Lagrange approach to electrodynamics in terms of intensities (without using the Aμ potentials as variation variables). The laws mentioned are derived according to Noether theorem because symmetry to which such concervation laws correspond is lost during the transition from intensities to potentials. Based on Noether theorem (and its generalization for Naeik's symmetries) and Lagrange function scalar in relation to complete Poincare group in terms of intensity tensor, a convenient formula for calculating and values conserved for electromagnetic field is derived which sets up a physically adequate symmetry operator -conservation law correlation and thus links the presence of conservation laws of polarized character with symmetry properties of Maxwell equations. Adiabaticity of conservation laws of polarized character under the presence of interaction with currents and charges is indicated