## 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 [X^{1},X^{2}, ......,X^{n}] and the poly-vector valued coordinates
X^{123...n} in noncommutative Clifford spaces is explicitly derived
and is given by [X^{1},X^{2}, ......,X^{n}] = n! X^{123...n}. It is argued how the
large N limit of n-ary commutators of n hyper-matrices X_{i1}_{i2}...._{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

**Download:** **PDF**

### Submission history

[v1] 11 Jan 2010

**Unique-IP document downloads:** 186 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.*

*
*