THE EQUIVALENCE PRINCIPLE OF QUANTUM-MECHANICS - UNIQUENESS THEOREM

Recently we showed that the postulated diffeomorphic equivalence of st ates implies quantum mechanics. This approach takes the canonical vari ables to be dependent by the relation p = partial derivative(q)L(o) ex ploits a basic GL(2,C)-symmetry which underlies the canonical formalis m. In particular, we looked far the special transformations leading to the free system with vanishing energy. Furthermore, we saw that while on the one hand the equivalence principle cannot be consistently impl emented in classical mechanics, on the other it naturally led to the q uantum analogue of the Hamilton-Jacobi equation, thus implying the Sch rodinger equation. In this letter we show that actually the principle uniquely leads to this solution. Furthermore, we find the map reducing any system to the free one with vanishing energy and derive the trans formations on L-o leaving the wave function invariant. We also express the canonical and Schrodinger equations by means of the brackets rece ntly introduced in the framework of N=2 SYM. These brackets are the an alogue of the Poisson brackets with the canonical variables taken as d ependent. (C) 1998 Published by Elsevier Science B.V. All rights reser ved.