Holonomies in quantum gravity

E.E. Wood

( Department of Physics, Monash University, Clayton, Vic. 3168, Australia )

Abstract

The holonomy loop representation has been utilised in 3+1 canonical quantum gravity so as to provide solutions to the canonical constraint equations. These solutions have a particularly elegant form in that they are solutions within knot classes. Motivated by this we propose a generalisation of the holonomy loop approach. To introduce this new approach we employ a more general notion of a Lie gauge group, namely a Lie gauge groupoid. We discuss the mathematical properties possessed by a field theory with groupoid as opposed to group structure and briefly discuss its advantages and hence our hopes for its applications in solving the problem of quantum gravity.