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

X. Shen, X. J. Wang

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 fe…