  The dynamics of supercooled liquid and glassy systems are usually studied
within the Lagrangian representation, in which the positions and velocities of
distinguishable interacting particles are followed. Within this representation,
however, it is difficult to define measures of spatial heterogeneities in the
dynamics, as particles move in and out of any one given region within long
enough times. It is also non-transparent how to make connections between the
structural glass and the spin glass problems within the Lagrangian formulation.
We propose an Eulerian formulation of supercooled liquids and glasses that
allows for a simple connection between particle and spin systems, and that
permits the study of dynamical heterogeneities within a fixed frame of
reference similar to the one used for spin glasses. We apply this framework to
the study of the dynamics of colloidal particle suspensions for packing
fractions corresponding to the supercooled and glassy regimes, which are probed
via confocal microscopy.
