Local Gauge Fields based on Gauge Theories in Loop Space

摘要

We consider a U(1) gauge theory and a Yang-Mills theory that are defined in the loop space (the space of all loops in space-time). From the U(1) gauge theory, we derive a local field theory of the abelian second-rank antisymmetric tensor field (Kalb-Ramond field) and the Stueckelberg formalism for a massive vector field. From the Yang-Mills theory in loop space, we derive the usual Yang-Mills theory and a non-abelian Stueckelberg formalism extended to local antisymmetric and symmetric tensor fields of the second rank. A coupling of local Yang-Mills fields and the abelian second-rank antisymmetric tensor field is also discussed on the basis of a unification of the Yang-Mills and U(1) gauge theories in loop space.