Do we have a consistent non-adiabatic quantum-classical mechanics?

Quantum-classical equations of motion satisfying Jacobi identity were recently proposed by V. V. KISIL ( Europhys. Lett., 72 ( 2005) 873), generalizing the Heisenberg group formulation of quantum mechanics. In the attempt to provide a physical interpretation for the resulting quantum-classical dynamics, we have reconstructed and analyzed the derivation, finding that there is a suitable representation from which the purely classical nature of the supposedly quantum-classical equations of motion clearly emerges. Copyright (C) EPLA, 2007.