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 {bold B}({bold r})={bold (}0,0,{ital B}({bold r}){bold )}, where {ital B}({bold r}){ge}0 or {ital B}({bold r}){le}0 and {bold r} is a point in the {ital xy} plane. Bounds are also obtained for the induced spin for (2+1)-dimensional QED in the presence of {bold B}({bold 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 {bold B}({bold r}) on R{sup 3}. {copyright} {ital 1996 The American Physical Society.}