Path Integral for Composite Fermions in the Half-filled Lowest Landau Level

We consider electrons in two dimensions in a strong magnetic field at half filling of the lowest Landau level using the Chern-Simons approach. Starting from a lattice Hamiltonian for the electrons, we derive a path integral (PI) formulation for the composite fermions (CF) which respects the order of the operators. We use a time lattice with intermediate times in order to have a PI expressed in density fluctuations. This formulation reveals that there is no infrared (IR) singularity in the grand-canonical potential in lowest order perturbation theory.