Quantum Mechanics on the Circle and W_{1+\INFTY}
arXiv:hep-th/9111053 · doi:10.1016/0370-2693(91)91323-N
Abstract
The algebra W_{1+\infty} with central charge c=0 can be identified with the algebra of quantum observables of a particle moving on a circle. Mathematically, it is the universal enveloping algebra of the Euclidean algebra in two dimensions. Similarly, the super W_\infty algebra is found to be the universal enveloping algebra of the super-Euclidean algebra in two dimensions.
(8 pages)