Quantum gravity in the Eddington purely affine picture
It was shown by Kijowski and Tulczjew that pure gravity with a cosmological constant can be obtained by a covariant Legendre transformation of a purely affine Lagrangian ''in the manner of Eddington'' constructed from a symmetric linear connection. In this paper I prove by explicit calculations that the Eddington Lagrangian is equivalent, in the sense which gives the same field equations, to a polynomial effective Lagrangian which turns out to be power-counting renormalizable. Then a formal proof of the unitarity of this theory is stated in the Kugo-Ojima formalism on the basis of the existence of two local Becchi-Rouet-Stora symmetries. These supertransformations are related to the algebra of the diffeomorphisms of the space-time, as well as to that of the volume-preserving space-time transformations which are not fixed by the gauge fixing used for the diffeomorphism group itself. Furthermore, I find that in the purely affine picture quantum gravity exhibits an infrared freedom. Since now the self-coupling constant is given by the cosmological constant, such a property could explain the observed almost zero value of the cosmological term at very large distances, i.e., to very low energies.
- Research Organization:
- The Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom
- OSTI ID:
- 6568462
- Journal Information:
- Phys. Rev. D; (United States), Vol. 29:12
- Country of Publication:
- United States
- Language:
- English
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
QUANTUM GRAVITY
COSMOLOGICAL MODELS
COUPLING CONSTANTS
FIELD EQUATIONS
HAMILTONIANS
LAGRANGIAN FUNCTION
METRICS
RENORMALIZATION
SPACE-TIME
EQUATIONS
FIELD THEORIES
FUNCTIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
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