Open String Star as a Continuous Moyal Product

Details Open String Star as a Continuous Moyal Product Open String Star as a Continuous Moyal Product

2002-02-14

arxiv.org/abs/hep-th/0202087v2

JHEP 0204 (2002) 022

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, LaTeX. One reference added

Scientific paper

10.1088/1126-6708/2002/04/022

We establish that the open string star product in the zero momentum sector can be described as a continuous tensor product of mutually commuting two dimensional Moyal star products. Let the continuous variable $\kappa \in [~0,\infty)$ parametrize the eigenvalues of the Neumann matrices; then the noncommutativity parameter is given by $\theta(\kappa) =2\tanh(\pi\kappa/4)$. For each $\kappa$, the Moyal coordinates are a linear combination of even position modes, and the Fourier transform of a linear combination of odd position modes. The commuting coordinate at $\kappa=0$ is identified as the momentum carried by half the string. We discuss the relation to Bars' work, and attempt to write the string field action as a noncommutative field theory.

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