Asymptotic estimates in quantum electrodynamics. II

The order of growth of the fermion determinant in quantum electrodynamics, $\det (\stackrel{/}{p}-e\stackrel{/}{A})$, as an entire function of $e$ is reconsidered. This order is of utmost importance in the high-order estimates of the perturbative expansion in QED. Explicit examples and some general arguments lead us to the conclusion that this determinant is generally of order 4 in four dimensions. The behavior ${\alpha }^n\left(\frac{n}{2}\right)!{\mathrm{}(-a)\mathrm{}}^n$ of the nth order of perturbation theory follows, disregarding ultraviolet problems.