Index of subfactors and statistics of quantum fields. I

We identify the statistical dimension of a superselection sector in a local quantum field theory with the square root of the index of a localized endomorphism of the quasi-local C^*-algebra that represents the sector. As a consequence in a two-dimensional theory the possible values of the statistical dimension below 2 are restricted to a given discrete set.Supported in part by Ministero della Pubblica Istruzione and CNR-GNAFA