Soluble Models of Quantum Gravitation

Abstract

The quantum theory of gravitation has essentially all the difficulties of conventional field theories, as well as several of its own. Among the latter are the technical difficulties of gauge aspects, constraints and positivity requirements on the metric, and the conceptual difficulties of interpretation. No lesser theory can describe the gravitational field. Nevertheless, considerable insight may frequently be gained by studying models exhibiting some of the distinctive features. The prime example of this is the electromagnetic field which is frequently used to gain insight into the properties of gauge freedoms. Other theories or models can shed light onto the difficulties associated with the positivity requirements on the metric tensor; for example, the space-like metric ${g_{{rs}}}\left( {\mathop{x}\limits_{\sim } } \right)$, when viewed as a 3 × 3 matrix, is positive definite.