  The construction of pointlike fields in quantum integrable models is usually
approached by constructing their n-point functions. However, convergence
questions of the resulting infinite series remain unresolved even in the
simplest case of the massive Ising model. On the other hand, the C*-algebraic
approach to the construction considers semi-local bounded operators, but yields
local operators only in a very abstract way.
  We use a novel approach to investigate the structure of these local
observables, in the form of smeared pointlike quantum fields. Instead of
considering their n-point functions and verifying the Wightman axioms, we
establish them as closed operators affiliated with the local C*-algebras.
  We explicitly construct all pointlike fields of the Ising model, verify the
Reeh-Schlieder property and show that they generate the local algebras by
dualization.
