Structural consequences of the coupling of gravitons

Abstract

The hypothetical but in string theories predicted gravitons and their allied quanta of the linearized gravitation field G yield, when coupled with other particles T, a remarkable structure of the entire state space S and an autonomous concept of observables. It is shown that S is spanned by a family of continuously many, pairwise orthogonal, pre-Hilbert spaces, called sectors. Each sector is the tensor product of an eigenspace of the operator of the 4-momentum distribution within the state space of T, and a corresponding eigenspace within the state space of G, both with any spatial distribution of the total 4-momentum as the eigenvalue 4-vector. Thus the states from any sector and so far the entirety of 4-momentum densities appear to be inseparably dressed by the quanta of G. Probably this dressing contributes to the dark matter. Furthermore, the special structure of the sectors lead to an own concept of observables, all of which commute from the beginning with the operator of the 4-momentum distribution.