Fock representations of ZF algebras and R-matrices

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 F S (H) are shown to satisfyand R (on K ⊗ K). This analysis generalises the well-known structure of Bose/Fermi Fock spaces and a recent result of Pennig.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.

Yang–Baxter endomorphisms

“…For example, in topological quantum computation, they may serve as quantum gates [6,43,56], and in the context of integrable quantum field theories on two-dimensional Minkowski space, unitary solutions of a more involved YBE involving a spectral parameter play the role of twoparticle collision operators [1]. Unitary solutions of (1.1), without spectral parameter, then describe the structure of short-distance scaling limits of such theories [46].…”

Yang-Baxter endomorphisms

“…For example, in topological quantum computation they serve as quantum gates [KL04,BG06,RW12], and in the context of integrable quantum field theories on two-dimensional Minkowski space, unitary solutions of a more involved Yang-Baxter equation involving a spectral parameter play the role of two-particle collision operators [AAR01]. Unitary solutions of (1.1), without spectral parameter, then describe the structure of short distance scaling limits of such theories [LS19].…”