  In this paper, we will present analytic formulas to express one-loop
contributions to lepton flavor violating decays $e_b\to e_a \gamma$, which are
also relevant to the anomalous dipole magnetic moments of charged leptons
$e_a$. These formulas were computed in the unitary gauge, using the well-known
Passarino-Veltman notations. We also show that our results are consistent with
those calculated previously in the 't Hooft-Veltman gauge, or in the limit of
zero lepton masses. At the one-loop level, we show that the appearance of
fermion-scalar-vector type diagrams in the unitary gauge will violate the Ward
Identity relating to an external photon. As a result, the validation of the
Ward Identity guarantees that the photon always couples with two identical
particles in an arbitrary triple coupling vertex containing a photon.
