We analyze the role played by local translational symmetry in the context of gauge theories of fundamental interactions. Translational connections and fields are introduced, with special attention being paid to their universal coupling to other variables, as well as to their contributions to field equations and to conserved quantities.
This is a very brief report on the attempts to introduce the concepts of noncommutative geometry in the theoretical description of the fundamental interactions. A particular emphasis will be given to gauge theories. A large part of the report is based on some on-going work in collaboration with Prof. Manolis Floratos. The main results have already been published[1], but there are many open problems remaining.
TRANSLATIONS AND DYNAMICS