Quantum Gravity and String Theory


On N-ary Algebras, Polyvector Gauge Theories in Noncommutative Clifford Spaces and Deformation Quantization

Authors: Carlos Castro

Polyvector-valued gauge field theories in noncommutative Clifford spaces are presented. The noncommutative binary star products are associative and require the use of the Baker-Campbell-Hausdorff formula. An important relationship among the n-ary commutators of noncommuting spacetime coordinates [X1,X2, ......,Xn] and the poly-vector valued coordinates X123...n in noncommutative Clifford spaces is explicitly derived and is given by [X1,X2, ......,Xn] = n! X123...n. It is argued how the large N limit of n-ary commutators of n hyper-matrices Xi1i2....in leads to Eguchi-Schild p-brane actions when p+1 = n. A noncomutative n-ary generalized star product of functions is provided which is associated with the deformation quantization of n-ary structures. Finally, brief comments are made about the mapping of the Nambu-Heisenberg n-ary commutation relations of linear operators into the deformed Nambu-Poisson brackets of their corresponding symbols.

Comments: 13 Pages. This article has been submitted to Physics Letters B

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Submission history

[v1] 11 Jan 2010

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