Entropy using Path Integrals for Quantum Black Hole Models
  Several eigenvalue equations that could describe quantum black holes have been proposed in the canonical quantum gravity approach. In this paper, we choose one of the simplest of these quantum equations to show how the usual Feynman's path integral method can be applied to obtain the corresponding statistical properties. We get a logarithmic correction to the Bekenstein-Hawking entropy as already obtained by other authors by other means. 
O. Obregon, M. Sabido, and V. I. Tkach