TOPOLOGICAL CHARGE ON THE LATTICE - A FIELD-THEORETICAL VIEW OF THE GEOMETRICAL APPROACH

We construct sequences of ''field theoretical'' lattice topological ch arge density operators which formally approach geometrical definitions in 2D CPN-1 models and 4D SU(N) Yang-Mills theories. The analysis of these sequences of operators suggests a new way of looking at the geom etrical method, showing that geometrical charges can be interpreted as limits of sequences of field theoretical (analytical) operators. In p erturbation theory, renormalization effects formally tend to vanish al ong such sequences. But, since the perturbative expansion is asymptoti c, this does not necessarily lead to well-behaved geometrical limits. It indeed leaves open the possibility that non-perturbative renormaliz ations survive. (C) 1997 Elsevier Science B.V.