  We discuss what can be learned about unparticle physics by studying simple
quantum field theories in one space and one time dimension. We argue that the
exactly soluble 2D theory of a massless fermion coupled to a massive vector
boson, the Sommerfield model, is an interesting analog of a Banks-Zaks model,
approaching a free theory at high energies and a scale invariant theory with
nontrivial anomalous dimensions at low energies. We construct a toy standard
model coupling to the fermions in the Sommerfield model and study how the
transition from unparticle behavior at low energies to free particle behavior
at high energies manifests itself in interactions with the toy standard model
particles.
