  We recall that in order to obtain the classical limit of quantum mechanics
one needs to take the $\hbar\rightarrow 0$ limit. In addition, one also needs
an explanation for the absence of macroscopic quantum superposition of position
states. One possible explanation for the latter is the Ghirardi-Rimini-Weber
(GRW) model of spontaneous localisation. Here we describe how spontaneous
localisation modifies the path integral formulation of density matrix evolution
in quantum mechanics. (Such a formulation has been derived earlier by Pearle
and Soucek; we provide two new derivations of their result). We then show how
the von Neumann equation and the Liouville equation for the density matrix
arise in the quantum and classical limit, respectively, from the GRW path
integral. Thus we provide a rigorous demonstration of the quantum to classical
transition.
