Let A be a local conformal net of von Neumann algebras on S-1 and rho a Mobius covariant representation of A, possibly with infinite dimension. If rho has finite index, rho has automatically positive energy. If rho 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 Mobius covariant left inverse. As a consequence the class of sectors with positive energy is stable under composition, conjugation and direct integral decomposition.

Bertozzini, P., Conti, R., Longo, R. (1998). Covariant sectors with infinite dimension and positivity of the energy. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 193(2), 471-492.

Covariant sectors with infinite dimension and positivity of the energy

LONGO, ROBERTO
1998-01-01

Abstract

Let A be a local conformal net of von Neumann algebras on S-1 and rho a Mobius covariant representation of A, possibly with infinite dimension. If rho has finite index, rho has automatically positive energy. If rho 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 Mobius covariant left inverse. As a consequence the class of sectors with positive energy is stable under composition, conjugation and direct integral decomposition.
1998
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
QUANTUM-FIELD THEORY; LOCAL OBSERVABLES; PARTICLE STATISTICS; EXISTENCE; SPIN
Bertozzini, P., Conti, R., Longo, R. (1998). Covariant sectors with infinite dimension and positivity of the energy. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 193(2), 471-492.
Bertozzini, P; Conti, R; Longo, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/54266
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