First Steps to a Theory of Quantum Gravity

This chapter covers the attempt to quantise general relativity, through a reformulation in terms of the Ashtekar variables. These are introduced, and the role and significance of the Barbero-Immirzi parameter is explored. The attempt to find a basis of states for quantum spacetime which satisfy the Hamiltonian, diffeomorphism, and Gauss constraints is used to motivate the choice of loop variables, from which loop quantum gravity gets its name.