Bosonisation of the Complex-boson realisation of $W_{\infty }$

Abstract

We bosonise the complex-boson realisations of the $W_{\infty }$ and $W_{1+\infty }$ algebras. We obtain nonlinear realisations of $W_{\infty }$ and $W_{1+\infty }$ in terms of a pair of fermions and a real scalar. By further bosonising the fermions, we then obtain realisations of $W_{\infty }$ in terms of two scalars. Keeping the most non-linear terms in the scalars only, we arrive at two-scalar realisations of classical $w_{\infty }$.

arXiv comment13 pages

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