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Conservation of Gravitational Energy Momentum and Renormalizable Quantum Theory of Gravitation

DOI: 10.4236/jmp.2013.48A013, PP. 133-152

Keywords: Path Integral Quantization, Gauge Theory, Volume-Preserving Diffeomorphisms

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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.


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