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EnglishIn 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 tthe 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.
| Titolo: | Determinants, pfaffians and quasi-free state representations of the CAR algebra |
| Autori: | |
| Data di pubblicazione: | 1998 |
| Rivista: | |
| 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 tthe 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. |
| Handle: | http://hdl.handle.net/11562/393131 |
| Appare nelle tipologie: | 01.01 Articolo in Rivista |
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