  We give a simple and direct construction of a massless quantum field with
arbitrary discrete helicity that satisfies Wightman axioms and the
corresponding relativistic wave equation in the distributional sense. We
underline the mathematical differences to massive models. The construction is
based on the notion of massless free net (cf. Section 3) and the detailed
analysis of covariant and massless canonical (Wigner) representations of the
Poincare' group. A characteristic feature of massless models with nontrivial
helicity is the fact that the fibre degrees of freedom of the covariant and
canonical representations do not coincide. We use massless relativistic wave
equations as constraint equations reducing the fibre degrees of freedom of the
covariant representation. They are characterized by invariant (and in contrast
with the massive case non reducing) one-dimensional projections. The definition
of one-particle Hilbert space structure that specifies the quantum field uses
distinguished elements of the intertwiner space between E(2) (the two-fold
cover of the 2-dimensional Euclidean group) and its conjugate.
  We conclude with a brief comparison between the free nets constructed in
Section 3 and a recent alternative construction that uses the notion of modular
localization.
