About the Relativist Framework of Quantum Theory

In previous papers, we have developed several considerations about the extension of the relativist quantum theory to the domain of superluminal velocities. In the present work, we propose a way to extend the relativist quantum theory to the framework of the general theory of Relativity.

Obviously any use of a three dimensional space (plus the time dimension) requires a geometry, but in usual quantum theories the space geometry is always Euclidean.

The generalization of a discrete space derivative equation from 1 to 3 dimensions with the usual space operators (gradient, curl, Laplacian) contains the implicit hypothesis of a Euclidean space. Thus we can explicitly propose the hypothesis of the Riemann's geometry which leads to a generalization of quantum theory to the framework of the general theory of Relativity.