  We propose that the boson peak originates from the (quasi-) localized
vibrational modes associated with long-lived locally favored structures, which
are intrinsic to a liquid state and are randomly distributed in a sea of
normal-liquid structures. This tells us that the number density of locally
favored structures is an important physical factor determining the intensity of
the boson peak. In our two-order-parameter model of the liquid-glass
transition, the locally favored structures act as impurities disturbing
crystallization and thus lead to vitrification. This naturally explains the
dependence of the intensity of the boson peak on temperature, pressure, and
fragility, and also the close correlation between the boson peak and the first
sharp diffraction peak (or prepeak).
