Maxwell’s Equations, Fields or Potentials?

Abstract

Abstract Fields and potentials of Maxwell’s Equations transform differently under the Lorentz transformation. Electric and magnetic fields are tridimensional objects which transform like massless fields as a subgroup of the Lorentz group. On the other hand, potentials are four-vectors. Therefore interactions of the electromagnetic fields with four-currents of massive particles cannot be achieved with fields, but only with potentials. Thus potentials seemed to be preferable and a correction to Maxwell’s equations seemed unavoidable. We have generalized the Maxwell’s equations, with 4-vector fields to allow interaction with currents. We suggest a new way to define the potentials and relate them to the new fields.