  To study composite fermions around an even denominator fraction, we adapt the
phase space single-particle path integral technique for interacting electrons
in zero magnetic field developed recently by D.S. Golubev and A.D. Zaikin,
Phys. Rev. B {\bf 59}, 9195 (1999). This path integral description gives an
intuitive picture of composite fermion propagation very similar to the
Caldeira-Leggett treatment of a particle interacting with an external
environment. We use the new description to explain the origin of the famous
cancellation between the self-energy and the vertex corrections in
semi-classical transport measurements. The effective range of the cancellation
is given by the size of the propagating particle, which for the Coulomb
interaction scales with the temperature T as T^{-1/4} |log T|^{-1} in the
semi-classical limit. Using this scheme we find that the effective mass in the
semi-classical limit for composite fermions in GaAs is approximately 6 times
the bare mass.
