# Conformal covariance of massless free nets

June 16, 2000

In the present paper we review in a fibre bundle context the covariant and
massless canonical representations of the Poincare' group as well as certain
unitary representations of the conformal group (in 4 dimensions). We give a
simplified proof of the well-known fact that massless canonical representations
with discrete helicity extend to unitary and irreducible representations of the
conformal group mentioned before. Further we give a simple new proof that
massless free nets for any helicity value are covariant under the conformal
group. Free nets are the result of a direct (i.e. independent of any explicit
use of quantum fields) and natural way of constructing nets of abstract
C*-algebras indexed by open and bounded regions in Minkowski space that satisfy
standard axioms of local quantum physics. We also give a group theoretical
interpretation of the embedding ${\mathfrak I}$ that completely characterizes the
free net: it reduces the (algebraically) reducible covariant representation in
terms of the unitary canonical ones. Finally, as a consequence of the conformal
covariance we also mention for these models some of the expected algebraic
properties that are a direct consequence of the conformal covariance (essential
duality, PCT--symmetry etc.).

Keywords:

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