On n-ary Algebras, Branes and Polyvector Gauge Theories in Noncommutative Clifford Spaces
by Carlos Castro
Center for Theoretical Studies of Physical Systems
Clark Atlanta University, Atlanta, GA. 30314; firstname.lastname@example.org
Submitted to the Journal of Math Phys
Polyvector-valued gauge field theories in noncommutative Clifford spaces are presented. The noncommutative star products are associative and require the use of the Baker-Campbell-Hausdorff formula. Actions for pbranes in noncommutative (Clifford) spaces and noncommutative phase spaces are provided. An important relationship among the n-ary commutators of noncommuting spacetime coordinates [X1,X2, ……,Xn] with the poly-vector valued coordinates X123…n in noncommutative Clifford spaces is explicitly derived [X1,X2, ……,Xn] = n! X123…n. The large N limit of n-ary commutators of n hyper-matrices Xi1i2….in leads to Eguchi-Schild p-brane actions for p + 1 = n. Noncommutative Clifford-space gravity as a poly-vector-valued gauge theory of twisted diffeomorphisms in Clifford spaces would require quantum Hopf algebraic deformations of Clifford algebras.
Source: 24 Sep. 2009, email by C. Castro (czarlosromanov_at_yahoo.com)