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We consider two theorems formulated in the derivation of the QuantumHamilton-Jacobi Equation from the EP. The first one concerns the proof that thecocycle condition uniquely defines the Schwarzian derivative. This isequivalent to show that the infinitesimal variation of the stress tensor"exponentiates" to the Schwarzian derivative. The cocycle condition naturallydefines the higher dimensional version of the Schwarzian derivative suggestinga role in the transformation properties of the stress tensor in higherdimensional CFT. The other theorem shows that energy quantization is a directconsequence of the existence of the quantum Hamilton-Jacobi equation underduality transformations as implied by the EP.

The cocycle of the quantum HJ equation and the stress tensor of CFT