The role of the $CP(N-1)$ geometry in the intrinsic unification of the general relativity and QFT

Abstract

Einstein's program of the unified field theory transformed nowadays to the TOE requiring new primordial elements and relations between them. Definitely, they must be elements of the quantum nature. One of most fundamental quantum elements are pure quantum states. Their basic relations are defined by the geometry of the complex projective Hilbert space. In the framework of such geometry all physical concepts should be formulated and derived in the natural way. Analysis following this logic shows that inertia and inertial forces are originated not in space-time but it the space of quantum states since they are generated by the deformation of quantum states as a reaction on an external interaction or self-interaction. In particular, inertia law generalized by Einstein during development of general relativity (GR) will be expressed in intrinsic quantum terms. It is assumed that quantum formulation of the inertia law should clarify the old problem of inertial mass (dynamical mass generation). The conservation of energy-momentum following form this law has been applied to self-interacting quantum Dirac's electron.