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On p-branes and antisymmetric non-Abelian tensorial gauge field theories of diffeomorphisms

Abstract:

It is shown how actions corresponding to antisymmetric non-Abelian tensorial gauge field theories of (p+1)-dimensional diffeomorphisms yield p-brane actions associated with their (p+1)-dimensional worldvolume evolution. We conclude with a discussion of how to obtain p-brane actions from the large N limit of covariant matrix models based on generalized hypermatrices. A deformation quantization of Nambu classical mechanics furnishing Nambu quantum mechanics by constructing the n-ary noncommutative product of n functions f 1 ·f2 · ⋯ ·fn, the n-ary version of the Moyal bracket, and the analog of the Weyl-Wigner- Groenowold-Moyal map among operators and c-functions remains an open problem. A solution to this problem will reveal important relations between the physics of p-branes and matrix models based on generalized hypermatrices in the large N limit. © 2011 World Scientific Publishing Company.