DIMENSIONAL REDUCTION OF U(1)XSU(2) CHERN-SIMONS BOSONIZATION - APPLICATION TO THE T-J MODEL

We perform a dimensional reduction of the U(1) x SU(2) Chem-Simons bos onization and we apply it to the t-J model relevant model for high T-c superconductors. This procedure yields a decomposition of the electro n field into the product of two ''semionic'' fields, i.e. fields obeyi ng abelian braid statistics with statistics parameter theta = 1/4, one carrying the charge and the other the spin degrees of freedom. A mean -field theory is then shown to reproduce correctly the large-distance behaviour of the correlation functions of the 1D t-J model at t much g reater than J. This results shows that to capture the essential physic al properties of the model one needs a specific ''semionic'' form of s pin-charge separation.