We consider conformal nets on S-1 of von Neumann algebras, acting on the full Fock space, arising in Free Probability. These models are twisted local, but non-local. We extend to the non-local case the general analysis of the modular structure. The local algebras turn out to be III1-factors associated with free groups. We use our setup to show examples exhibiting arbitrarily large maximal temperatures, but failing to satisfy the split property, then clarifying the relation between the latter property and the trace class conditions on e(-betaL), where L is the conformal Hamiltonian.

D'Antoni, C., Longo, R., Radulescu, F. (2001). Conformal nets, maximal temperature and models from free probability. JOURNAL OF OPERATOR THEORY, 45(1), 195-208.

Conformal nets, maximal temperature and models from free probability

LONGO, ROBERTO;RADULESCU, FLORIN
2001-01-01

Abstract

We consider conformal nets on S-1 of von Neumann algebras, acting on the full Fock space, arising in Free Probability. These models are twisted local, but non-local. We extend to the non-local case the general analysis of the modular structure. The local algebras turn out to be III1-factors associated with free groups. We use our setup to show examples exhibiting arbitrarily large maximal temperatures, but failing to satisfy the split property, then clarifying the relation between the latter property and the trace class conditions on e(-betaL), where L is the conformal Hamiltonian.
2001
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
von Neumann algebras; free probability; conformal quantum field theory; nuclearity; split
14
http://www.theta.ro/jot/archive/2001-045-001/2001-045-001-010.pdf
D'Antoni, C., Longo, R., Radulescu, F. (2001). Conformal nets, maximal temperature and models from free probability. JOURNAL OF OPERATOR THEORY, 45(1), 195-208.
D'Antoni, C; Longo, R; Radulescu, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/54270
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