  We develop a quantum replica method for interacting particle systems and use
it to estimate the location of the glass transition line in Helium 4. Although
we do not fully succeed in taking into account all quantum effects, we make a
thorough semiclassical analysis. We confirm previous suggestions that quantum
fluctuations promote the formation of the glass and give a quantitative
estimate of this effect at high density. Finally, we discuss the difficulties
that are met when one tries to extend the calculation to the region of low
densities and low temperatures, where quantum effects are strong and the
semiclassical expansion breaks down.
