Physics – Mathematical Physics
Scientific paper
2000-06-16
Rev.Math.Phys. 13 (2001) 1135-1162
Physics
Mathematical Physics
31 pages, Latex2e
Scientific paper
10.1142/S0129055X01000958
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 ${\got I}$ 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.).
Lledo Fernando
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