Quantum Gravity as a Theory of Connections

Consider the interior of a black hole or the very early universe: matter is so densely localized that neither the effects of gravity nor those of quantum theory can be ignored. But this entails that neither general relativity nor quantum theory on its own can fully describe such a situation, for some of the most fundamental principles inhering in these two theories are haunted by the specter of incompatibility. Quantum gravity is the name for the bewildering penumbra of theories that seek to exorcise this demon. But it turns out that the metrical variables of general relativity constitute a lamp too narrow to bottle the phantom, and loop quantum gravity is a fascinating enterprise that seeks the Aladdin who does possess the required lamp. This is achieved by recasting general relativity as a theory of connections, rather than that of metrics. This shift of emphasis allows one to use a number of mathematical tools that make it possible to arrive at a fully consistent, almost background-independent theory of quantum gravity. This thesis endeavours to probe these ideas in detail.