  We provide a theoretical description for the coupling between the
intersubband excitations of a bi-dimensional electron gas with the
electromagnetic field. This description, based on the electrical dipole gauge,
applies to an arbitrary quantum heterostructure embedded in a general
multilayered waveguide or a microcavity. We show that the dipole gauge
Hamiltonian automatically takes into account the Coulomb interactions in this
system. Furthermore, it can be conveniently expressed in terms of the many-body
collective plasmon modes, which interact both with each other and with the
light field. The dipole gauge therefore provides a suitable framework for the
study of solid state Quantum Electrodynamics (QED) phenomena, such as the
ultra-strong light-matter interaction regime, occurring at very high electronic
densities.
