  We consider two theorems formulated in the derivation of the Quantum
Hamilton-Jacobi Equation from the EP. The first one concerns the proof that the
cocycle condition uniquely defines the Schwarzian derivative. This is
equivalent to show that the infinitesimal variation of the stress tensor
"exponentiates" to the Schwarzian derivative. The cocycle condition naturally
defines the higher dimensional version of the Schwarzian derivative suggesting
a role in the transformation properties of the stress tensor in higher
dimensional CFT. The other theorem shows that energy quantization is a direct
consequence of the existence of the quantum Hamilton-Jacobi equation under
duality transformations as implied by the EP.
