Induced gravity and the gauge technique

The apparent incompatibility of the quantum theory with general relativity is well known. In this thesis we consider a possible solution to this problem, namely the program of induced gravity. The problem of quantum gravity, namely its nonrenormalizability, is due to its scale non-invariance. The assumption of the induced gravity program is to begin with a fundamental scale invariant Lagrangian which is renormalizable. Quantum fluctuations can break scale invariance and thus it is possible that the Einstein-Hilbert Lagrangian will be induced, as first shown by Sakharov. This breaking of a classical symmetry by quantum fluctuations is called dynamical symmetry breaking. It is possible to derive a relation between the induced Newtonian gravitational constant, G, and the stress-energy tensor of the matter fields. This formula, due to Adler and Zee, is derived. A review is given of all previous model calculations of G and their successes and failures noted. The extension to a quantized metric is considered and the properties of the scale invariant fundamental gravitational Lagrangian are studied. Since the idea of inducing gravity as a quantum effect is essentially a non-perturbative effect, we require non-perturbative techniques to obtain useful information. One such technique is the Delbourgo-Salam Gauge Technique. A review of this technique is given, followed by its application to the program of induced gravity. The philosophy of this ansatze is used to calculate an approximation to the contribution to G from a general fermiongraviton theory in terms of the spectral function of the fermion. The details of the Gauge Technique are then used to perform an actual calculation of the contribution to G from QED. The result is quite small, signifying that the contribution to G from the electrodynamic interactions of the low mass fermions does not lead to any unexpected surprises.