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arXiv · hep-th/0504160

Comment on the Surface Exponential for Tensor Fields

E. T. Akhmedov·V. Dolotin·A. Morozov
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Abstract

Starting from essentially commutative exponential map $E(B|I)$ for generic tensor-valued 2-forms $B$, introduced in \cite{Akh} 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 ${\cal E}(B|I|t_γ)$, 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 $I_{ijk}$, associated with the structure constants of {\it 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).

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E. T. Akhmedov, V. Dolotin, A. Morozov. 2005-04-19. Comment on the Surface Exponential for Tensor Fields. https://doi.org/10.1134/1.2034595

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