AXIOMATIC HOLONOMY MAPS AND GENERALIZED YANG-MILLS MODULI SPACE

This Letter is a follow-up of Barrett, J. W., Internat. J. Theoret. Ph ys. 30(9),(1991). Its main goal is to provide an alternative proof of that part of the reconstruction theorem which concerns the existence o f a connection. A construction of a connection 1-form is presented. Th e formula expressing the local coefficients of the connection in terms of the holonomy map is obtained as an immediate consequence of that c onstruction. Thus, the derived formula coincides with that used in Cha n, H.-M., Scharbach, P., and Tsou, S. T., Ann. Physics 166, 396-421 (1 986). The reconstruction and representation theorems form a generaliza tion of the fact that the pointed configuration space of the classical Yang-Mills theory is equivalent to the set of all holonomy maps. The point of this generalization is that there is a one-to-one corresponde nce not only between the holonomy maps and the orbits in the space of connections, but also between all maps OMEGAM --> G fulfilling some ax ioms and all possible equivalence classes of P(M, G) bundles with conn ections, where the equivalence relation is defined by a bundle isomorp hism in a natural way.