  The covariant quantization of the electromagnetic field in the Lorentz gauge
gives rise to longitudinal and scalar photons in addition to the usual
transverse photons. It is shown here that the exchange of longitudinal and
scalar photons can produce entanglement between two distant atoms or harmonic
oscillators. The form of the entangled states produced in this way is very
different from that obtained in the Coulomb gauge, where the longitudinal and
scalar photons do not exist. A generalized gauge transformation is used to show
that all physically observable effects are the same in the two gauges, despite
the differences in the form of the entangled states. An approach of this kind
may be useful for a covariant description of the dynamics of quantum
information processing.
