Superselection Sectors in Asymptotic Quantization of Gravity

Abstract

Using the continuity of the scalar $Ψ_2$ (the mass aspect) at null infinity through $i_o$ we show that the space of radiative solutions of general relativity can be thought of a fibered space where the value of $Ψ_2$ at $i_o$ plays the role of the base space. We also show that the restriction of the available symplectic form to each ``fiber'' is degenerate. By finding the orbit manifold of this degenerate direction we obtain the reduced phase space for the radiation data. This reduced phase space posses a global structure, i.e., it does not distinguishes between future or past null infinity. Thus, it can be used as the space of quantum gravitons. Moreover, a Hilbert space can be constructed on each ``fiber'' if an appropriate definition of scalar product is provided. Since there is no natural correspondence between the Hilbert spaces of different foliations they define superselection sectors on the space of asymptotic quantum states.