  Motivated by the appearance of a `reflection symmetry' in transport
experiments and the absence of statistical periodicity in relativistic quantum
field theories, we propose a series of relativistic composite fermion theories
for the compressible states appearing at filling fractions $\nu=1/2n$ in
quantum Hall systems. These theories consist of electrically neutral Dirac
fermions attached to $2n$ flux quanta via an emergent Chern-Simons gauge field.
While not possessing an explicit particle-hole symmetry, these theories
reproduce the known Jain sequence states proximate to $\nu=1/2n$, and we show
that such states can be related by the observed reflection symmetry, at least
at mean field level. We further argue that the lowest Landau level limit
requires that the Dirac fermions be tuned to criticality, whether or not this
symmetry extends to the compressible states themselves.
