Quantum Gravity and String Theory


On n-ary Algebras, Branes and Polyvector Gauge Theories in Noncommutative Clifford Spaces

Authors: Carlos Castro

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.

Comments: 25 Pages. This article has been submitted to the J. Math. Phys.

Download: PDF

Submission history

[v1] 24 Sep 2009

Unique-IP document downloads: 171 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.

comments powered by Disqus