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Conservation of Gravitational Energy Momentum and Renormalizable Quantum Theory of Gravitation

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DOI: 10.4236/jmp.2013.48A013    4,638 Downloads   5,962 Views   Citations

ABSTRACT

Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energymomentum naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner Minkowski space which can describe gravitation at the classical level. This theory is quantized in the path integral formalism starting with a non-covariant Hamiltonian formulation with unconstrained canonical field variables and a manifestly positive Hamiltonian. The relevant path integral measure and weight are then brought into a Lorentz- and gauge-covariant form allowing to express correlation functions—applying the De Witt-Faddeev-Popov approach—in any meaningful gauge. Next the Feynman rules are developed and the quantum effective action at one loop in a background field approach is renormalized which results in an asymptotically free theory without presence of other fields and in a theory without asymptotic freedom including the Standard Model (SM) fields. Finally the BRST apparatus is developed as preparation for the renormalizability proof to all orders and a sketch of this proof is given.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

C. Wiesendanger, "Conservation of Gravitational Energy Momentum and Renormalizable Quantum Theory of Gravitation," Journal of Modern Physics, Vol. 4 No. 8A, 2013, pp. 133-152. doi: 10.4236/jmp.2013.48A013.

References

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