A path integral approach for the colloidal glass transition based on an analogy with the $\lambda$-transition in liquid helium

We describe a model for the colloidal glass transition that is based on Feynman's theory for the $\lambda$-transition in liquid helium. Our model essentially counts the number of configurations of dynamic loops, strings or clusters of different sizes, and determines the glass transition volume fraction $\phi_{g}$ from the distribution of these heterogeneities. Since confinement restricts the available number of configurations for these loops, strings and clusters, its effect on $\phi_{g}$ can also be calculated in a relatively straightforward manner.