Fock representations of ZF algebras and R-matrices

Lechner G, Scotford C (2020)

Publication Type: Journal article

Publication year: 2020


Book Volume: 110

Pages Range: 1623-1643

Journal Issue: 7

DOI: 10.1007/s11005-020-01271-3


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).

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Lechner, G., & Scotford, C. (2020). Fock representations of ZF algebras and R-matrices. Letters in Mathematical Physics, 110(7), 1623-1643.


Lechner, Gandalf, and Charley Scotford. "Fock representations of ZF algebras and R-matrices." Letters in Mathematical Physics 110.7 (2020): 1623-1643.

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