GENERALIZED CONFORMAL SYMMETRY AND EXTENDED OBJECTS FROM THE FREE PARTICLE

The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these sys tems outside the critical values of the anomaly leads to a new degree of freedom which shares its internal character with spin, but neverthe less features an infinite number of different states. Both are associa ted with the transformation properties of wave functions under the Wey l-symplectic group WSp(6, R). The physical meaning of this new degree of freedom can be established, with a major scope, only by analyzing t he quantization of an infinite-dimensional algebra of diffeomorphisms generalizing string symmetry and leading to more general extended obje cts.