QED in inhomogeneous magnetic fields

A lower bound is placed on the fermionic determinant of Euclidean quantum electrodynamics in three dimensions in the presence of a smooth, finite-flux, static, unidirectional magnetic field B(r) = (0,0,B(r)), where B(r)greater than or equal to 0 or B(r)less than or equal to 0 and r is a point in the xy plane. Bounds are also obtained for the induced spin for (2+1)-dimensional QED in the presence of B(r). An upper bound is placed on the fermionic determinant of Euclidean QED in four dimensions in the presence of a strong, static, directionally varying, square-integrable magnetic field B(r) on R(3).