Global one-dimensionality conjecture within quantum general relativity

Lukasz Andrzej Glinka1

Abstract

A simple quantum gravity model, based on a new conjecture within the canonically quantized 3 + 1 general relativity, is presented. The conjecture states that matter fields are functionals of an embedding volume form only and reduces to quantum geometrodynamics. By dimensional reduction the resulting theory is presented in the form of the Dirac equation, and application of the Fock quantization with the diagonalization procedure yields construction of the appropriate quantum field theory. The 1D wave function is derived, the corresponding 3-dimensional manifolds are discussed as well as physical scales associated with quantum correlations.

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