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arXiv · hep-th/0103176

A suggestion for an integrability notion for two dimensional spin systems

Harald Grosse·Karl-Georg Schlesinger
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Abstract

We suggest that trialgebraic symmetries migth be a sensible starting point for a notion of integrability for two dimensional spin systems. For a simple trialgebraic symmetry we give an explicit condition in terms of matrices which a Hamiltonian realizing such a symmetry has to satisfy and give an example of such a Hamiltonian which realizes a trialgebra recently given by the authors in another paper. Besides this, we also show that the same trialgebra can be realized on a kind of Fock space of q-oscillators, i.e. the suggested integrability concept gets via this symmetry a close connection to a kind of noncommutative quantum field theory, paralleling the relation between the integrability of spin chains and two dimensional conformal field theory.

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Harald Grosse, Karl-Georg Schlesinger. 2001-03-21. A suggestion for an integrability notion for two dimensional spin systems. https://arxiv.org/abs/hep-th/0103176

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