NEW LOOP REPRESENTATIONS FOR 2+1-GRAVITY

Since the gauge group underlying (2 + 1)-dimensional general relativit y is noncompact, certain difficulties arise in the passage from the co nnection to the loop representations. It is shown that these problems can be handled by appropriately choosing the measure that features in the definition of the loop transform. Thus, 'old-fashioned' loop repre sentations-based on ordinary loops-do exist. In the case when the spat ial topology is that of a 2-torus, these can be constructed explicitly ; all quantum states can be represented as functions of (homotopy clas ses of) loops and the scalar product and the action of the basic obser vables can be given directly in terms of loops.