  We study a 2+1 dimensional theory of bosons and fermions with an omega ~ k^2
dispersion relation. The most general interactions consistent with specific
symmetries impart fractional statistics to the fermions. Unlike examples
involving Chern-Simons gauge theories, our statistical phases derive from the
exchange of gapless propagating bosons with marginal interactions. Even though
no gap exists, we show that the anyonic statistics are precisely defined.
Symmetries combine with the vacuum structure to guarantee the
non-renormalization of our anyonic phases.
