Abstract
Representation of the algebra of FP (anti)ghosts in string theory is studied by generalizing the recursive fermion system in the Cuntz algebra constructed previously. For that purpose, the pseudo-Cuntz algebra, which is a *-algebra generalizing the Cuntz algebra and acting on indefinite-metric vector spaces, is introduced. The algebra of FP (anti)ghosts in string theory is embedded into the pseudo-Cuntz algebra recursively in two different ways. Restricting a certain permutation representation of the pseudo-Cuntz algebra, representations of these two recursive FP ghost systems are obtained. With respect to the zero-mode operators of FP (anti)ghosts, it is shown that one corresponds to the four-dimensional representation found recently by one of the present authors (M. Abe) and Nakanishi, while the other corresponds to the two-dimensional one by Kato and Ogawa.
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