Toward a Theory of Non-Abelian Tensor Fields

We present a triangulation-independent area-ordering prescription that naturally generalizes the well-known path-ordering prescription. For such a prescription, it is natural that the two-form “connection” carries three “color” indices rather than two, as is the case with the ordinary one-form gauge connection. To define this prescription, we must define exponentiation of a matrix with three indices. The definition uses the fusion-rule structure constants.