Abstract
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of covariant quantum gravity (CQG-theory). The treatment is founded on the recently identified Hamiltonian structure associated with the classical space-time, i.e., the corresponding manifestly covariant Hamilton equations and the related Hamilton–Jacobi theory. The quantum Hamiltonian operator and the CQG-wave equation for the corresponding CQG-state and wave function are realized in 4-scalar form. The new quantum wave equation is shown to be equivalent to a set of quantum hydrodynamic equations which warrant the consistency with the classical GR Hamilton–Jacobi equation in the semiclassical limit. A perturbative approximation scheme is developed, which permits the adoption of the harmonic oscillator approximation for the treatment of the Hamiltonian potential. As an application of the theory, the stationary vacuum CQG-wave equation is studied, yielding a stationary equation for the CQG-state in terms of the 4-scalar invariant-energy eigenvalue associated with the corresponding approximate quantum Hamiltonian operator. The conditions for the existence of a discrete invariant-energy spectrum are pointed out. This yields a possible estimate for the graviton mass together with a new interpretation about the quantum origin of the cosmological constant.
Highlights
IntroductionDistinctive features of covariant quantum gravity (CQG)-theory presented here are that, just like the CCG-theory (i.e., the theory of covariant classical gravity) developed in Part 1, realizing a canonical quantization approach for SF-GR, it satisfies the principles of general covariance and manifest covariance
Distinctive features of covariant quantum gravity (CQG)-theory presented here are that, just like the CCG-theory developed in Part 1, realizing a canonical quantization approach for SF-GR, it satisfies the principles of general covariance and manifest covariance
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of covariant quantum gravity (CQG-theory)
Summary
Distinctive features of CQG-theory presented here are that, just like the CCG-theory (i.e., the theory of covariant classical gravity) developed in Part 1, realizing a canonical quantization approach for SF-GR, it satisfies the principles of general covariance and manifest covariance. This means that—in comparison with customary literature canonical quantization approaches to SF-GR [6,7]—the theory proposed here preserves its form under arbitrary local point transformations. Consistent with the same principles, first it is based on the adoption of 4-tensor continuum Lagrangian coordinates and canonical momentum operators and a manifestly covariant quantum wave equation referred to here as CQG-wave equation. Its formulation is of general validity, i.e., it applies to arbitrary possible realizations of the underlying classical space-time
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