Abstract
ABSTRACT. The exactly solvable vacuum polarization by an external constant electromagnetic field is examined. It is proven that the Stieltjes type continued fraction corresponding to the divergent perturbation expansion in the general case does not converge to the exact solution, the convergence taking place only for the vacuum polarization for a pure electric or a pure magnetic field. The summability of the perturbation expansion to the exact solution under the Borei method is also proven. In this communication some results will be reported concerning the divergent perturbation expansion of the vacuum polarization by an external constant electromagnetic field and its summability to the exact solution through the Stieltjes type continued fraction and the (generalized) Borei method. The proof of the statements presented can be found in [1] and [2]. The complete Lagrangian due to the vacuum polarization by an external constant electromagnetic field, as it has been computed by Schwinger [3] reads: (1) L=-F-L
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