Symmetry in Nonlinear Mathematical Physics - 2009
Eyo Ita (United States Naval Academy, Annapolis, USA & University of Cambridge, UK)
Finite states in four dimensional quantized gravity
The criterion for finiteness stems from a precise cancellation of the ultraviolet singularities stemming from the quantum
Hamiltonian constraint, allowing for an exact solution. This signifies the following developments for 4D QGRA:
The aforementioned algorithm is designed to construct explicit solutions to the constraints of the full theory by inspection, while implementing any desired ‘boundary’ conditions on the states necessary to reduce to the appropriate semiclassical limit. Conversely, the finite states of 4D QGRA can place severe restrictions on phenomena occurring in the weak gravitational limit below the Planck scale.
While we demonstrate this for the GKodS in this talk, the procedure can be applied to obtain a family of states labeled by two arbitrary functions of position, which possess the requisite Hilbert space structure in the limit where the matter fields are turned off. Remaining areas of research in progress include the illumination of the Hilbert space structure of the GKodS, analysis of various models for which the SQC can produce tractable solutions, in the full theory and in minisuperspace, and the addressal of any issues of interest regarding the mathematical rigor of the states.