We define a fixed point topological charge for the two–dimensional O(3) lattice σ–model which is free of topological defects. We use this operator in combination with the fixed point action to measure the topological susceptibility for a wide range of correlation lengths. The results strongly suggest that it is not a physical quantity in this model. The procedure, however, can be applied to oth...

in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...

On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the continuum. The prerequisite for that is the construction of continuum gauge fields from lattice gauge fields. Such a construction, which is gauge covariant an...

To check the consistency of positivity requirements for the two-point correlation function of the topological charge density, which were identified in a previous paper, we are computing perturbatively this twopoint correlation function in the two-dimensional O(3) model. We find that at the one-loop level these requirements are fulfilled.