Fock representations of ZF algebras and R-matrices

Lechner, Gandalf ORCID: https://orcid.org/0000-0002-8829-3121 and Scotford, Charley 2020. Fock representations of ZF algebras and R-matrices. Letters in Mathematical Physics 110 , pp. 1623-1643. 10.1007/s11005-020-01271-3

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Abstract

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. These representations are motivated from quantum field theory (short-distance scaling limits of integrable models).

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer Verlag (Germany)
ISSN:	0377-9017
Date of First Compliant Deposit:	9 March 2020
Date of Acceptance:	12 February 2020
Last Modified:	06 Jan 2024 04:24
URI:	https://orca.cardiff.ac.uk/id/eprint/130191

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