Nonlinear Phenomena in Complex Systems, 2014, Vol.17, No.4, pp.372-376

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2014, Vol.17, No.4, pp.372-376

On Precanonical Quantization of Gravity
I. V. Kanatchikov

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 different points of space-time, which obey the covariant precanonical analogue of the Schrödinger 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.

Key words: precanonical quantization, quantum gravity, De Donder–Weyl Hamiltonization

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