Loop formulation of gauge theory and gravity

Abstract

This chapter contains a overview of the loop formulation of Yang-Mills theory and 3+1-dimensional gravity in the Ashtekar form. Since the configuration space of these theories are spaces of gauges potentials, their classical and quantum descriptions may be given in terms of gauges-invariant Wilson loops. I discuss some mathematical problems that arise in the loop formulation and illustrate parallels and difference between the gauge theoretic and gravitational applications. Some remarks are made on the discretized lattice approach.