  We discuss the derivation of the electrodynamics of superconductors coupled
to the electromagnetic field from a Lorentz-invariant bosonic model of Cooper
pairs. Our results are obtained at zero temperature where, according to the
third law of thermodynamics, the entropy of the system is zero. In the
nonrelativistic limit we obtain a Galilei-invariant superconducting system
which differs with respect to the familiar Schr\"odinger-like one. From this
point of view, there are similarities with the Pauli equation of fermions which
is derived from the Dirac equation in the nonrelativistic limit and has a
spin-magnetic field term in contrast with the Schr\"odinger equation. One of
the peculiar effects of our model is the decay of a static electric field
inside a superconductor exactly with the London penetration length. In
addition, our theory predicts a modified D'Alembert equation for the massive
electromagnetic field also in the case of nonrelativistic superconducting
matter. We emphasize the role of the Nambu-Goldstone phase field which is
crucial to obtain the collective modes of the superconducting matter field. In
the special case of a nonrelativistic neutral superfluid we find a gapless
Bogoliubov-like spectrum, while for the charged superfluid we obtain a
dispersion relation that is gapped by the plasma frequency.
