Proceedings of the Steklov Institute of Mathematics

, Volume 272, Issue 1, pp 169–176

An affinity for affine quantum gravity

Article

DOI: 10.1134/S0081543811010159

Cite this article as:
Klauder, J.R. Proc. Steklov Inst. Math. (2011) 272: 169. doi:10.1134/S0081543811010159

Abstract

The main principle of affine quantum gravity is the strict positivity of the matrix \(\{ \hat g_{ab} (x)\} \) composed of the spatial components of the local metric operator. Canonical commutation relations are incompatible with this principle, and they can be replaced by noncanonical, affine commutation relations. Due to the partial second-class nature of the quantum gravitational constraints, it is advantageous to use the projection operator method, which treats all quantum constraints on an equal footing. Using this method, enforcement of regularized versions of the gravitational constraint operators is formulated quite naturally as a novel and relatively well-defined functional integral involving only the same set of variables that appears in the usual classical formulation. Although perturbatively nonrenormalizable, gravity may possibly be understood nonperturbatively from a hard-core perspective that has proved valuable for specialized models.

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Department of Physics and Department of MathematicsUniversity of FloridaGainesvilleUSA