  The definitions of the effective mass of the composite fermion are discussed
for the half-filled Landau level problem. In a recent work, Shankar and Murthy
show a finite effective mass of the composite fermion by a canonical
transformation while the perturbative calculation gives the logarithmic
divergence of the effective mass at the Fermi surface. We will emphasize that
the different definition of the effective mass has the different physical
processes. The finite one could be defined for any momentum of the composite
fermion while the divergence only appears at the Fermi surface. We work with
the standard Halperin-Lee-Read model but in the temporal gauge. The advantage
of this gauge to be employed is that the finite effective mass could be
calculated in the Hartree-Fock approximation. Furthermore, it is precisely
equal to the result that Shankar and Murthy obtained which is well-fit with the
numerical calculation from the ground state energy analysis and a
semi-classical estimation. However, if we consider the random phase
approximation, one sees that the divergence of the effective mass of the
quasiparticle at the Fermi surface emerges again no matter that we work on the
temporal or Coulomb gauges. We develop an effective theory where the finite
effective mass serves as a `bare' effective mass and show that the same
divergence of the RPA effective mass. On the other hand, the correct behavior
of the response functions in the small band mass limit could be seen clearly in
the temporal gauge since there is a self-interaction among the magnetoplasmons.
