Yang-Baxter Algebra for the n-Harmonic Oscillator Realisation of sp(2n,R)
Abstract
Using a rational R-matrix associated with the 4 x 4 defining matrix representation of c2=sp(4), the Lie algebra of Sp(4), a one-site operator solution of the associated Yang-Baxter algebra acting in the Fock space of two harmonic oscillators is derived. This is used to define N-site integrable systems, which are soluble by a version of the algebraic Bethe ansatz method without nesting. All essential aspects of the work generalise directly from c2 to cn.
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