Isaac Scientific Publishing

Advances in Astrophysics

Reduced Quantum General Relativity in Higher Dimensions

Download PDF (463.4 KB) PP. 86 - 92 Pub. Date: August 1, 2016

DOI: 10.22606/adap.2016.12003

Author(s)

  • Lukasz Andrzej Glinka*
    Independent Science Editor & Author, Non-fiction & Philosophy Writer, Poland; Member, American Association of International Researchers, USA
  • Patrick Linker
    M.Sc. Student, Fachgebiet Kontinuumsmechanik, Technische Universität Darmstadt, 64287 Darmstadt, Germany

Abstract

Quantum General Relativity of a higher dimensional Riemannian manifold being an embedded space in a space-time being a Lorentzian manifold is investigated through a technique of differential topology. Consequently, in the reduced model of quantum geometrodynamics, the Wheeler-DeWitt equation is replaced through a first order functional quantum evolution and a supplementary eigenequation for a scalar curvature of an embedded space. The phenomenological approach, in the framework of objective quantum gravity and global one-dimensional conjecture, is applied in order to make the standard formalism of quantum mechanics applicable to quantum gravity, beyond a Feynman path integral and a Wilson loop techniques. It leads to the wave function which refers to quantum tunnelling through a manifestly exponential form and is determined through energy density of matter fields and a cosmological constant, and physical interpretation of quantum gravity through the Tomonaga-Schwinger equation and the Dirac interaction picture of relativistic quantum mechanics. The resulting model of quantum gravity creates the opportunity of potentially new theoretical and phenomenological applications for astrophysics, cosmology, and physics.

Keywords

quantum gravity, quantum geometrodynamics, Wheeler-DeWitt equation, phenomenological approach, objective quantum gravity, global one-dimensional conjecture, differential topology, quantum tunnelling, Tomonaga-Schwinger equation

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