Galilean Geometry in Condensed Matter Systems

In this thesis we present a systematic means to impose Galilean invariance within effective field theory. Recently a number of authors have shown that Galilean invariance has powerful consequences on condensed matter systems. However, unlike the relativistic case, torsion is often a necessary element and is subject to constraints that make it surprisingly difficult to include in a Galilean invariant way. We will review this issue, define the most general torsionful geometries consistent with Galilean invariance and then turn to applications within effective field theory and the quantum Hall effect.