MASSIVE SCHWINGER MODEL AND 4-DIMENSIONAL QED - THE CONNECTION

We state the connection between the fermion determinant in four-dimensional QED (QED4) and the massive Schwinger model, QED2, for the case of smooth, polynomial-bounded, unidirectional magnetic fields. Using the diamagnetic bound on the fermion determinant in QED2, we obtain an upper bound on the fermion determinant in QED4 for this class of fields. Using Kato's inequality, we obtain an upper bound on the one-loop effective action in scalar QED4 for smooth, polynomial-bounded but otherwise general fields with fast decrease at infinity.