Equivalence principle, higher-dimensional Mobius group and the hidden antisymmetric tensor of quantum mechanics

We show that the recently formulated equivalence principle (EP) implies a b asic cocycle condition both in Euclidean and Minkowski spaces, which holds in any dimension. This condition, that in one dimension is sufficient to fi x the Schwarzian equation, implies a fundamental higher-dimensional Mobius invariance which, in turn, unequivocally fixes the quantum version of the H amilton-Jacobi equation. This also holds in the relativistic case, so that we obtain both the time-dependent Schrodinger equation ana the Klein-Gordon equation in any dimension. We then show that the EP implies that masses ar e related by maps induced by the coordinate transformations connecting diff erent physical systems. Furthermore, we show that the minimal coupling pres cription, and therefore gauge invariance, arises quite naturally in impleme nting the EP. Finally, we show that there is an antisymmetric 2-tensor whic h underlies quantum mechanics and sheds new light on the nature of the quan tum Hamilton-Jacobi equation.