Authors: Carlos Castro
Starting with a brief review of our prior construction of $n$-ary algebras, based on the relation among the {\bf n}-ary commutators of noncommuting spacetime coordinates $ [ X^1, X^2, ......, X^n ] $ with the polyvector valued coordinates $X^{123 ...n} $ in noncommutative Clifford spaces, $ [ X^1, X^2, ......, X^n ] = n ! ~X^{123 ...n} $, we proceed to construct generalized brane actions in noncommutative matrix coordinates backgrounds in Clifford-spaces ($C$-spaces). An instrumental role is played by the Clifford-valued field $\Phi (\sigma^A) = \Phi^M (\sigma^A) \Gamma_M $ which allows to construct a matrix realization of the $n$-ary algebra of the form $ {\bf X}^M \equiv \Phi^{ -1} ( \sigma^A) \Gamma^M \Phi (\sigma^A) $, and that is given in terms of the world manifold's $\sigma^A$ polyvector-valued coordinates of the generalized brane, and which by construction, $satisfy$ the $n$-ary algebra. One then learns that is the presence of matter which $endows$ the spacetime points with a noncommutative algebraic structure. We finalize with an extension of coherent states in $ C$-spaces and provide a preliminary study of strings in target $C$-space backgrounds.
Comments: 18 Pages.
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[v1] 2022-04-04 04:48:24
[v2] 2022-06-07 19:11:04
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