GENERALIZED HOLONOMIES

We study some issues related to the notion of generalized holonomies, providing a rigorous mathematical framework where we discuss early heu ristic ideas from the physics literature, mainly due to R. Gambini and his collaborators, who have tried to formulate an ''extended loop rep resentation'' of quantum gravity in Ashtekar variables. We also define a EACH (Baker-Campbell-Hausdorff) series for the formal generalized h olonomy and prove its convergence in some particular cases. Finally, w e discuss the issue of covariance of generalized holonomies, and prove the covariance for nilpotent connections. Copyright (C) Elsevier Scie nce B.V.