Identities for the electron forms 2 and their 3D representation Original Research Article

New type of identities for products of the electron forms 2 (Fs2) and the bilinear forms (BFs) are derived. The identities are found for both temporal Fs2 describing the electron energy and quasi energy densities and spatial Fs2 describing the linear momentum and quasi linear momentum densities. The identities allow one to transform the quasi energy densities into the energy densities as well as the quasi linear momentum densities into the linear momentum densities. It is shown that by choosing any one of the 16 electron temporal or spatial Fs2 one can represent the remaining 15 temporal or spatial Fs2 as combinations of a chosen form 2 (F2) and the derivatives of a number of BFs. Any one of such 16 sets of identities can be considered as a specific form of an irreducible representation for the temporal or spatial Fs2. Similar to the bilinear identities for BFs the derived identities can be used for reduction different physical quantities describing the electron to the forms defined by the basic physical observables. As an example we consider transformation of the electron energy density to a new fundamental form that presents the energy density through the linear momentum density.