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

摘要

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