On Precanonical Quantization of Gravity

Abstract

Precanonical quantization is based on mathematical structures of the De Donder–Weyl Hamiltonization of field theories. The resulting formulation of quantum gravity describes the quantum geometry of space-time in terms of operator-valued distances and the transition amplitudes between the values of spin connection at di˙erent points of space-time, which obey the covariant precanonical analogue of the Schr¨odinger equation. In the context of quantum cosmology the theory predicts a probability distribution of a cosmological spin-connection field, which may have an observable impact on the large scale structures in the universe.