부산대학교 도서관

One of the commonly agreed-upon axioms of all mathematical models for physical phenomena is that infinity can only appear in the model as an unphysical, unreachable asymptotic sort of state. In particular, experimentally measurable things, such as charge, mass, and the like, cannot be infinite. \par This axiom formed the basis for the Born-Infeld model of electromagnetism, which sought to address the unphysical infinity in the self-energy of the electrostatic field that is introduced by using the basically empirical Coulomb law for a point-like mass. This infinity then prevented one from attributing the mass of a charged body with the potential energy of its electrostatic field. The idea was to make electric field strength bounded by some maximum field strength in the same way that the velocity of massive matter is bounded by the speed of light. This maximum field strength seems to be justified by the well-established phenomenon of pair production by sufficiently high energy and therefore high field strength photons. \par The article under review carries this analogy between spatial velocity vectors and field strength vectors further, by representing electric field strength vectors as boost transformations and magnetic field strength vectors as Euclidean rotations, so collectively an electromagnetic field defines an element of the Lorentz group. Consequently, the composition of boosts, which implies the relativistic formula for the addition of spatial velocities, gives a corresponding law for the addition of field strength vectors. \par The authors then show that one can obtain the Maxwell equations, as defined by a boosted observer, by taking the total time derivative of the element of the Lorentz group defined by an electromagnetic field and divergences of the resulting dynamical equations. \par They do this, first for the electrostatic field, which defines a pure boost, and then for the magnetic field, which defines a pure rotation, and then discuss its form for a radiation field, which involves both. They then suggest the proper form of an electromagnetic field strength tensor that one might use to extend the analysis to general relativity, instead of special relativity, although that analysis is deferred to a later work.