  A microscopic theory of optical transitions in quantum dots with
carrier-phonon interaction is developed. Virtual transitions into higher
confined states with acoustic phonon assistance add a quadratic phonon coupling
to the standard linear one, thus extending the independent Boson model. Summing
infinitely many diagrams in the cumulant, a numerically exact solution for the
interband polarization is found. Its full time dependence and the absorption
lineshape of the quantum dot are calculated. It is the quadratic interaction
which gives rise to a temperature-dependent broadening of the zero-phonon line,
being here calculated for the first time in a consistent scheme.
