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  Conformal covariance of massless free nets

Lledo, F. (2001). Conformal covariance of massless free nets. Reviews in Mathematical Physics, 13(9), 1135-1161.

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 Urheber:
Lledo, Fernando1, Autor
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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 Zusammenfassung: 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.).

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Sprache(n): eng - English
 Datum: 2001
 Publikationsstatus: Erschienen
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 Ort, Verlag, Ausgabe: -
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 Identifikatoren: eDoc: 2792
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Titel: Reviews in Mathematical Physics
Genre der Quelle: Zeitschrift
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Ort, Verlag, Ausgabe: -
Seiten: - Band / Heft: 13 (9) Artikelnummer: - Start- / Endseite: 1135 - 1161 Identifikator: -