Is the composite fermion a Dirac particle?

We propose a particle-hole symmetric theory of the Fermi-liquid ground state of a half-filled Landau level. This theory should be applicable for a Dirac fermion in magnetic field at charge neutrality, as well as for the nu=1/2 quantum Hall ground state of nonrelativistic fermions in the limit of negligible inter-Landau-level mixing. We argue that when particle-hole symmetry is exact, the composite fermion is a massless Dirac fermion, characterized by a Berry phase of ? around the Fermi circle. We write down a tentative effective field theory of such a fermion and discuss the physical consequences