Electromagnetic quantities in 4-D space and the dual Hodge operator

Two aspects of the presentation of electromagnetism in three-dimensional space can be compared if a distinction is made between polar vectors P and axial vectors T. In option α, Baldomir and Hammond take B, E, Dα , jα, Hα as basic vectors and need to use the *Hodge dual operator. Option β is presented based on the vectors B, E, Dβ, jβ, Hβ where no special operator is required. For the presentation of electromagnetism in four-dimensional space the components of the group E B, common to both options, are brought together to form a tensor of 4² = 16 components. The B_ij are arranged within a 3 × 3 square, with the E _k on the edge of this square. The slightly different forms of this arrangement correspond to the tensors identified symbolically by F _pq (B, E) for option α and F _km (B, E) for option β. Two Maxwell equations are related to the corresponding tensors for each option. For option β, a tensor G^km directly linked to F _km (B, E) naturally leads to Hβ and Dβ. The consideration of this tensor along with the four-dimensional current density vector J_β (expressed using jβ and ρ) allows one to establish the two other Maxwell equations