The Formal Structure of Quantum Gravity

Abstract

In 1956 Utiyama pointed out that the gravitational field can be regarded as a non-Abelian gauge field. In 1963 Feynman found that in order to construct a quantum perturbation theory for a non-Abelian gauge field he had to introduce new graphical rules not previously encountered in quantum field theory. He showed, in one-loop order, that to preserve unitarity one must add to every standard closed-loop graph another, involving a closed integral-spin fermion loop. In 1966 an explicitly gauge invariant functional-integral algorithm was found which extended Feynman’s new rules to all orders (De Witt (1967b)). A short time later it was shown that the algorithm could be obtained by a method of factoring out the gauge group (Fadde’ev and Popov (1967)).