Comments on the evaluation of the effective potential in quantum electrodynamics

We have checked the numerical results of the effective Lagrangian as a function of the field strengths H and E in the paper of Dittrich, Tsai, and Zimmermann on the evaluation of the effective potential in quantum electrodynamics. We present the more accurate numerical results and plots. The Euler-Heisenberg Lagrangian is non-negative, monotonically increasing, and does not exhibit a minimum as a function of the magnetic field in the range 0< or =H< or =0.35H/sub cr/. The real part of the effective Lagrangian has a minimum for the electric field approx. =3E/sub cr/approx. =5.125 x 1016 V/cm. Our numerical values of the effective Euler-Heisenberg Lagrangian are approximately two orders of magnitude smaller than the corresponding results of Dittrich et al. The phenomenon of spontaneous symmetry breaking does not occur either for a pure magnetic field or a pure electric field case