Covariant Sectors with Infinite Dimensionand Positivity of the Energy
Abstract
Let ? be a local conformal net of von Neumann algebras on S^{1} and ρ a Möbius 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 , or equivalently sectors with nonsolitonic 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 Möbius covariant left inverse. As a consequence the class of sectors with positive energy is stable under composition, conjugation and direct integral decomposition.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1998
 DOI:
 10.1007/s002200050337
 arXiv:
 arXiv:functan/9704007
 Bibcode:
 1998CMaPh.193..471B
 Keywords:

 Mathematics  Functional Analysis;
 High Energy Physics  Theory;
 Mathematics  Operator Algebras
 EPrint:
 25 pages, Latex2e