Abstract
In this paper we apply the theory of quasi-free states of CAR algebras and their Bogolubov automorphisms to give an alternative C*algebraic construction of the determinant and pfaffian line bundles discussed by Pressley-Segal
and by Borthwick. The basic property of the pfaffian of being the holomorphic
square root of the determinant bundle (after restriction to the isotropic grassmannian) is derived from a Fock-anti-Fock correspondence and
an application of the Powers-Stormer purification procedure. A Borel-Weil type description of the infinite dimensional Spin^c-representation is discussed, via a Shale-Stinespring implementation of Bogolubov transformations.
Lingua originale | English |
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pagine (da-a) | 705-721 |
Numero di pagine | 17 |
Rivista | Reviews in Mathematical Physics |
Volume | 10 |
Stato di pubblicazione | Pubblicato - 1998 |
Keywords
- Hilbert space grassmannian, CAR algebra, determinant and pfaffian bundles