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The definitions of the effective mass of the composite fermion are discussedfor the half-filled Landau level problem. In a recent work, Shankar and Murthyshow a finite effective mass of the composite fermion by a canonicaltransformation while the perturbative calculation gives the logarithmicdivergence of the effective mass at the Fermi surface. We will emphasize thatthe different definition of the effective mass has the different physicalprocesses. The finite one could be defined for any momentum of the compositefermion while the divergence only appears at the Fermi surface. We work withthe standard Halperin-Lee-Read model but in the temporal gauge. The advantageof this gauge to be employed is that the finite effective mass could becalculated in the Hartree-Fock approximation. Furthermore, it is preciselyequal to the result that Shankar and Murthy obtained which is well-fit with thenumerical calculation from the ground state energy analysis and asemi-classical estimation. However, if we consider the random phaseapproximation, one sees that the divergence of the effective mass of thequasiparticle at the Fermi surface emerges again no matter that we work on thetemporal or Coulomb gauges. We develop an effective theory where the finiteeffective mass serves as a `bare' effective mass and show that the samedivergence of the RPA effective mass. On the other hand, the correct behaviorof the response functions in the small band mass limit could be seen clearly inthe temporal gauge since there is a self-interaction among the magnetoplasmons.Comment: 27 pages,6 eps figure

Effective mass of composite fermions and fermionic Chern-Simons theory in the temporal gauge