  We reintroduce an alternative expression for the Lagrangian density that
governs the interaction of a charged particle with external electromagnetic
fields, proposed by Livens about one century ago. This Lagrangian is written in
terms of the local superposition of the particle fields with the applied
electromagnetic fields, not in terms of the particle charge and of the
electromagnetic potentials as is usual. Here we show that the total Lagrangian
for a set of charged particles assumes a simple elegant form with the
alternative formulation, giving an aesthetic support for it. We also show that
the alternative Lagrangian is equivalent to the traditional one in their domain
of validity and that it provides an interesting description of the
Aharonov-Bohm effect.
