Covariant Sectors with Infinite Dimension¶and Positivity of the Energy |
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Authors: | Paolo Bertozzini Roberto Conti Roberto Longo |
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Institution: | Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133 Roma, Italy.?E-mail: bertozzi@mat.uniroma2.it, conti@mat.uniroma2.it, longo@mat.uniroma2.it, IT
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Abstract: | Let ? be a local conformal net of von Neumann algebras on S
1 and ρ a M?bius covariant representation of ?, possibly with infinite dimension. If ρ has finite index, ρ has automatically
positive energy. If ρ has infinite index, we show the spectrum of the energy always to contain the positive real line, but,
as seen by an example, it may contain negative values. We then consider nets with Haag duality on ℝ, or equivalently sectors
with non-solitonic extension to the dual net; we give a criterion for irreducible sectors to have positive energy, namely
this is the case iff there exists an unbounded M?bius covariant left inverse. As a consequence the class of sectors with positive
energy is stable under composition, conjugation and direct integral decomposition.
Received: 21 April 1997 / Accepted: 23 September 1997 |
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