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
[v1] 11 Jan 2010
Unique-IP document downloads: 206 times
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.