The Metal-Insulator Transition in High-Tc Cuprates - An unusual Quantum Transition

The Hilbert spaces representing the quantum states in the CuO2 planes are not spanned by crystal symmetry adapted basis states, but by self-consistently renormalized states which form compound systems of Hilbert subspaces. In addition, these self-consistent basis representations are not necessarily stationary in time but behave dynamic in many respects. In particular, the coordinate systems of the Hilbert subspaces form a definite dynamic relative state in space and time, thus the coordinate system itself becomes a variable. This implicates a deterministic space-time relation of quantum states and the quantization of time by an internal time constant, the eigentime tau(eiDCBF). In undoped and hole doped CuO2 planes tau(eiDCBF) occurs as a conservation quantity, whereas under electron doping a partial fluid exists in which tau(eiDCBF) does not occur as quantized quantity. The deterministic space-time behaviour of the Hilbert subspaces represents the emergence of a classical space-time structure in quantum systems. The metal-insulator transition in high-T-c cuprates, usually attributed to an antiferromagnetic Mott transition, results here from an additional splitting into Hilbert subspaces. The transition from the insulator to the conductor is causally related to coordinate transformations from the copper to the oxygen sites. The antiferromagnetism in the CuO2 planes is not caused by the half-filled valence bands, as usually assumed, but is created by off-diagonal spin compensations within filled bands.