Stable extended particles in generalized electrodynamics

On the basis of the biquaternionic formalism, a Lorentz-invariant theory generalizing the classical Maxwell electrodynamics is developed. The theory is shown to be invariant with respect to the group U2, and just this invariance leads to the most important consequences. Among them the so-called ''self-equilibrium condition'', introduced by Milner in 1963, seems to be of particular importance. By using this condition several models of stable extended particles are elaborated, including those obtained previously by Milner. As a by-product, the classic Lorentz model of an extended electron is improved and replaced by a more realistic one. It is obtained a discrete series of particles, whose charges and masses are integral multiples of the smallest value, suggesting that not only just the electron but the whole family of leptons can be described within this theory