Quantum Gravity and Black Hole Entropy

The basic features of a quantum field theory which is Poincaré invariant, gauge invariant, finite and unitary to all orders of perturbation theory is reviewed. Quantum gravity is perturbatively finite and unitary to all orders of perturbation theory. The Bekenstein-Hawking entropy formula for a black hole is investigated in a conical Rindler space approximation to a black hole event horizon. A renormalization of the gravitational coupling constant is performed leading to a finite Bekenstein-Hawking entropy at the horizon. Invited talk given at the XI International Conference on Problems of Quantum Field Theory, July 13-17, 1998, Dubna, Russia. 1 Finite Quantum Field Theory A finite quantum field theory (FQFT) based on a nonlocal interaction Lagrangian has been developed which is perturbatively finite, unitary and gauge invariant [19]. The finiteness draws from the fact that factors of exp[K(p)/2ΛF ] are attached to propagators which suppress any ultraviolet divergences in Euclidean momentum space. An important development in FQFT was the discovery that gauge invariance and unitarity can be restored by adding series of higher interactions. The resulting theory possesses a nonlinear, field representation dependent gauge invariance which agrees with the original local symmetry on shell but is larger off shell. Quantization is performed in the functional formalism using an analytic and convergent measure factor which retains invariance under the new symmetry. An explicit calculation was made of the measure factor in QED[2], and it was obtained to lowest order in Yang-Mills theory[5]. Kleppe and Woodard[7] obtained an ansatz based on the derived dimensionally regulated result when ΛF → ∞, which was conjectured to lead to a general functional measure factor in FQFT gauge theories. A convenient formalism which makes the FQFT construction transparent is based on shadow fields[5, 7]. Let us denote by fi a generic local field and write the standard local action as W [f ] = WF [f ] +WI [f ], (1)