Commuting co-ordinates in the new field theory

In the preceding paper Born and Infeld introduce, besides the energy W, the momentum p and the angular momentum M of a closed electro-dynamical system, also the co-ordinates q of the energy centre, defined by qx= ½ (W-1 ξ x + ξx W-1), etc., (1.1) where ξx= ∫xT44dv, etc. (1.2) From these they derive an inner angular momentum, s, which is a property of the system, independent of the choice of the origin. These quantities have simple transformation properties: p and W form a four-vector pi; ξ — pt and M together form a six-vector Mik; Ws and — s·p form the four-vector si, given by si = Mki* pk. (Mki* is the dual of Mki.)