부산대학교 도서관

One of the commonly agreed-upon axioms of all mathematical models forphysical phenomena is that infinity can only appear in the model as anunphysical, unreachable asymptotic sort of state. In particular,experimentally measurable things, such as charge, mass, and the like,cannot be infinite.\parThis axiom formed the basis for the Born-Infeld model ofelectromagnetism, which sought to address the unphysical infinity inthe self-energy of the electrostatic field that is introduced by usingthe basically empirical Coulomb law for a point-like mass. Thisinfinity then prevented one from attributing the mass of a charged bodywith the potential energy of its electrostatic field. The idea was tomake electric field strength bounded by some maximum field strength inthe same way that the velocity of massive matter is bounded by thespeed of light. This maximum field strength seems to be justified bythe well-established phenomenon of pair production by sufficiently highenergy and therefore high field strength photons.\parThe article under review carries this analogy between spatial velocityvectors and field strength vectors further, by representing electricfield strength vectors as boost transformations and magnetic fieldstrength vectors as Euclidean rotations, so collectively anelectromagnetic field defines an element of the Lorentz group.Consequently, the composition of boosts, which implies the relativisticformula for the addition of spatial velocities, gives a correspondinglaw for the addition of field strength vectors.\parThe authors then show that one can obtain the Maxwell equations, asdefined by a boosted observer, by taking the total time derivative ofthe element of the Lorentz group defined by an electromagnetic fieldand divergences of the resulting dynamical equations.\parThey do this, first for the electrostatic field, which defines a pureboost, 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 strengthtensor that one might use to extend the analysis to general relativity,instead of special relativity, although that analysis is deferred to alater work.