Open String Star as a Continuous Moyal Product

Abstract

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.

30 pages, LaTeX. One reference added

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• Solving Open String Field Theory with Special Projectors
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