Commuting co-ordinates in the new field theory

Abstract

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 q x = ½ (W -1 ξ x + ξ x W -1 ), etc., (1.1) where ξ x = ∫ x T 44 dv , 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 p i ; ξ — p t and M together form a six-vector M ik ; Ws and — s·p form the four-vector s i , given by s i = M ki * p k . (M ki * is the dual of M ki .)