Quantum Theory of Gravity. III. Applications of the Covariant Theory
Abstract
The basic momentum-space propagators and vertices (including those for the fictitious quanta) are given for both the Yang-Mills and gravitational fields. These propagators are used to obtain the cross sections for gravitational scattering of two scalar particles, scattering of gravitons by scalar particles, graviton-graviton scattering, two-graviton annihilation of scalar-particle pairs, and graviton bremsstrahlung. Special features of these cross sections are noted. Problems arising in renormalization theory and the role of the Planck length are discussed. The gravitational Ward identity is derived, and the structure of the radiatively corrected 1-graviton vertex for a scalar particle is displayed. The Ward identity is only one of an infinity of identities relating the many-graviton vertex functions of the theory. The need for such identities may be eliminated in principle by computing radiative corrections directly in coordinate space, using the theory of manifestly covariant Green's functions. As an example of such a calculation, the contribution of conformal metric fluctuations to the vacuum-to-vacuum amplitude is summed to all orders. The physical significance of the renormalization terms is discussed. Finally, Weinberg's treatment of the infrared problem is examined. It is not difficult to show that the fictitious quanta contribute negligibly to infrared amplitudes, and hence that Weinberg's use of the DeDonder gauge is justified. His proof that the infrared problem in gravidynamics can be handled just as in electrodynamics is thereby made rigorous.
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Real-valued variables allow for the construction of a mathematically rigorous kinematical framework by means of which constraint operators can be regulated in a non-ambiguous fashion.
“The advantage of these real-valued variables is that they allow for the construction of a mathematically rigorous kinematical framework by means of which constraint operators can be regulated in a non-ambiguous fashion.”
From Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity (1996) · cites this paper as [4]
The validity of those prior operators relies heavily on the assumption that one can exponentiate the generator of the Wick transform as outlined in [4].
“Their validity relies heavily on the assumption that one can actually exponentiate the generator of the Wick transform as outlined in [4].”
From Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity (1996) · cites this paper as [4]
A solution to problem 1 has been suggested: one can define real Ashtekar variables which simplify the rescaled Hamiltonian constraint of Euclidean gravity and then construct a Wick rotation transform from the Euclidean to the Lorentzian regime where complex Ashtekar variables are needed to simplify the Lorentzian constraint.
“A solution to problem 1) has been suggested in [4] (see also [5]) : namely, one can define real Ashtekar variables [6] which simplify the rescaled Hamiltonian constraint of Euclidean gravity and then construct a Wick rotation transform from the Euclidean to the Lorentzian regime where the complex Ashtekar variables are needed to simplify the Lorentzian constraint.”
From Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity (1996) · cites this paper as [4]
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- Authors
- DeWitt, B. S.
- Affiliations
- University of North Carolina at Chapel Hill (US)
- Corresponding author
- DeWitt, Bryce S.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1967-10-25
- Volume
- 162
- Issue
- 5
- Pages
- 1239-1256
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W1974281514
- Cited by
- 980
- References
- 15
- Citations by year
- 2026: 9 · 2025: 29 · 2024: 33 · 2023: 38 · 2022: 29 · 2021: 37 · 2020: 44 · 2019: 39 · 2018: 51 · 2017: 26 · 2016: 17 · 2015: 23 · 2014: 13 · 2013: 21 · 2012: 19
- FWCI
- 14.74
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- quantum gravity, graviton propagator, renormalization, Planck length, radiative corrections, infrared problem, de Donder gauge
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