The symmetric states on a quasi local C*-algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend the De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki-Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self-containing interest.

Crismale, V., & Fidaleo, F. (2012). De Finetti Theorem on the CAR Algebra. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 315(1), 135-152 [10.1007/s00220-012-1506-z].

De Finetti Theorem on the CAR Algebra

FIDALEO, FRANCESCO
2012-10

Abstract

The symmetric states on a quasi local C*-algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend the De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki-Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self-containing interest.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
eng
Con Impact Factor ISI
Exchangeability; Noncommutative probability and statistics; C∗-algebras; States; Applications to quantum physics
http://link.springer.com/article/10.1007%2Fs00220-012-1506-z
Crismale, V., & Fidaleo, F. (2012). De Finetti Theorem on the CAR Algebra. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 315(1), 135-152 [10.1007/s00220-012-1506-z].
Crismale, V; Fidaleo, F
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
crifid1.pdf

non disponibili

Licenza: Copyright dell'editore
Dimensione 471.62 kB
Formato Adobe PDF
471.62 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/89957
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 14
social impact