Publication: Conformal covariance of massless free nets
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2001
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World Scientific Publishing
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Abstract
In the present paper we review in a fiber bundle context the covariant and massless canonical representations of the Poincaré 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 ℐ. that completely characterizes the free net: it reduces the (algebraically) reducible covariant representation in terms of the unitary canonical ones. Finally, we also mention some of the expected algebraic properties of these models that are a direct consequence of the conformal covariance (essential duality, PCT-symmetry etc).
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27 pages, no figures.-- MSC2000 codes: 81T05, 81S05, 81R40, 81R15, 81T40, 22D10, 22D12.-- Dedicated to Hellmut Baumgärtel on the occasion of his 65th birthday.
MR#: MR1853828 (2002j:81142)
Zbl#: Zbl 1029.81047
MR#: MR1853828 (2002j:81142)
Zbl#: Zbl 1029.81047
Keywords
Local quantum physics
Bibliographic citation
Reviews in Mathematical Physics, 2001, vol. 13, n. 9, p. 1135-1161