In gauge theories, physical histories are represented by space-time
connections modulo gauge transformations. The space of histories is thus
intrinsically non-linear. The standard framework of constructive quantum field
theory has to be extended to face these {\it kinematical} non-linearities
squarely. We first present a pedagogical account of this problem and then
suggest an avenue for its resolution.Comment: 27 pages, CGPG-94/8-2, latex, contribution to the Cambridge meeting
proceeding
