3 years ago

The quantum hydrodynamic representation in curved space and the related Einstein equation.

Piero Chiarelli

The work shows that the evolution of quantum states in the hydrodynamic representation can be obtained by Lagrangean motion equations that can be derived by a minimum action principle. Once the quantum hydrodynamic motion equations have been generalized in the non-Euclidean space-time by using the physics covariance postulate, the quantum gravity equation, determining the geometry of the space-time necessary to give full meaning to them, is obtained by minimizing the overall action comprehending the gravitational field. The theoretical output for a scalar uncharged field shows the spontaneous emergence of a cosmological energy impulse tensor density (CEITD) that in the classical limit converges to a constant. The mean value of CEITD in the galactic space leads to the correct order of magnitude of the cosmological constant. The coupling of the quantum gravitational equation with half-spin fermions is finally developed.

Publisher URL: http://arxiv.org/abs/1711.06093

DOI: arXiv:1711.06093v3

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