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Fock representations of Zamolodchikov algebras and R-matrices

Lechner, Gandalf and Scotford, Charley 2019. Fock representations of Zamolodchikov algebras and R-matrices. arXiv

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A variation of the Zamolodchikov-Faddeev algebra over a finite dimensional Hilbert space H and an involutive unitary R-Matrix S is studied. This algebra carries a natural vacuum state, and the corresponding Fock representation spaces FS(H) are shown to satisfy FS⊞R(H⊕K)≅FS(H)⊗FR(K), where S⊞R is the box-sum of S (on H⊗H) and R (on K⊗K). This analysis generalises the well-known structure of Bose/Fermi Fock spaces and a recent result of Pennig.\par It is also discussed to which extent the Fock representation depends on the underlying R-matrix, and applications to quantum field theory (scaling limits of integrable models) are sketched.

Item Type: Article
Date Type: Published Online
Status: Submitted
Schools: Mathematics
Publisher: Cornell University
ISSN: 2331-8422
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Last Modified: 18 Oct 2019 04:33

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