Group Theory and Gravity

Abstract

Although group theory has been of great success as applied to elementary particle physics, it has not been widely applied to gravitation. One notable exception concerns the conformal group on which Segal’s theory of Chapter 9 is based. This group has a substantial history of usage in gravitational field theory, and in this chapter discussions are given first of the applications of the conformal group and related topics and then of more general ways in which group theory and gravity might be connected. Particular attention is paid to theories which, while unproven for the most part, are of interest because they attempt to unite elementary particle theory and electromagnetism with gravitation, in contrast to the theories examined in Chapter 9 which are primarily accounts of the gravitational interaction alone.