  We develop a theory for the pseudorelativistic fractional quantum Hall effect
in graphene, which is based on a multicomponent abelian Chern-Simons theory in
the fermionic functional integral approach. Calculations are performed in the
Keldysh formalism, directly giving access to real-time correlation functions at
finite temperature. We obtain an exact effective action for the Chern-Simons
gauge fields, which is expanded to second order in the gauge field fluctations
around the mean-field solution. The one-loop fermionic polarization tensor as
well as the electromagnetic response tensor in random phase approximation are
derived, from which we obtain the Hall conductivities for various FQH states,
lying symmetrically around charge neutrality.
