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Statistical transmutation in diluted flux states.

We investigate a generalization of the commensurate-flux-state theory of the diluted t-J model in which fluctuations in the self-induced gauge field are coupled to the hole coordinates. Doped fermionic holes in the theory carry an internal SU(2)\ifmmode\times\else\texttimes\fi{}SU(2) degree of freedom, and a polarization of this internal field leads to fractionization of the quantum statistics of the particles. The many-semion states of the model are studied by an application of the Atiyah-Singer index theorem to investigate the dynamics of these diluted flux states.