Remarks on topological models and fractional statistics

One of the most intriguing aspects of Chern-Simons-type topological models is the fractional statistics of point particles which has been shown essent ial for our understanding of the fractional quantum Hall effects. Furthermo re these ideas are applied to the study of high Tc superconductivity. We pr esent here an recently proposed model for fractional spin with the Pauli te rm. On the other hand, in D=4 space-time, a Schwarz-type topological gauge theory with antisymmetric tensor gauge field, namely B boolean AND F model, is reviewed. Antisymmetric tensor fields are conjectured as mediator of st ring interaction. A dimensional reduction of the previous model provides a (2+1) dimensional topological theory, which involves a 2-form B and a 0-for m phi. Some recent results on this model are reported. Recently, there have been thoughts of generalizing unusual statistics to extended objects in ot hers space-time dimensions, and in particular to the case of strings in fou r dimensions. In this contest, discussions about fractional spin and antisy mmetric tensor field are presented.