Comment on the Surface Exponential for Tensor Fields

Starting from essentially commutative exponential map E(B|I) for generic tensor-valued 2-forms B, introduced in [1] as direct generalization of the ordinary non-commutative P -exponent for 1-forms with values in matrices (i.e. in tensors of rank 2), we suggest a non-trivial but multi-parametric exponential E(B|I|tγ), which can serve as an interesting multi-directional evolution operator in the case of higher ranks. To emphasize the most important aspects of the story, construction is restricted to backgrounds Iijk , associated with the structure constants of commutative associative algebras, what makes it unsensitive to topology of the 2d surface. Boundary effects are also eliminated (straightfoward generalization is needed to incorporate them).