On N-ary Algebras, Polyvector Gauge Theories in Noncommutative Clifford Spaces and Deformation Quantization
by Carlos Castro
Center for Theoretical Studies of Physical Systems
Clark Atlanta University, Atlanta, GA. 30314; perelmanc_at_hotmail.com
submitted to Phys. Letts B
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 X^123…n in noncommutative Clifford spaces is explicitly derived and is given by [X1,X2, ……,Xn] = n! X^123…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.
Source: Email by C. Castro of 13 Jan. 2010, http://www.vixra.org/pdf/1001.0016v1.pdf