  A systematic formalism for quantum electrodynamics in a classical uniform
magnetic field is discussed. The first order radiative correction to the ground
state energy of an electron is calculated. This then leads to the anomalous
magnetic moment of an electron without divergent integrals. Thorough analyses
of this problem are given for the weak magnetic field limit. A new expression
for the radiative correction to the ground state energy is obtained. This
contains only one integral with an additional summation with respect to each
Landau level. The importance of this formalism is also addressed in order to
deal with quantum electrodynamics in an intense external field.
