Lowest-Order Gravitational Interactions

Abstract

Having investigated the significance of lowest-order covariant Feynman “tree” (no loop) diagrams for strong, electromagnetic, and weak interactions, it is quite natural to try to extend the approach to the fourth fundamental force, that of gravity. The problem is that the gravitational interaction is so weak that quantum gravity corrections to the classical force will, in all likelihood, never be detected. Moreover, like the current-current weak interaction, higher order corrections are usually divergent. Thus, the major justification for looking at quantum gravity is that it may give us a deeper understanding of the classical newtonian force, and if a unified theory of forces is ever developed in detail, it most certainly will have to include the gravitational interaction. Accordingly, we attempt to construct quantum “graviton” wave functions, propagators, vertices, Feynman rules and diagrams in the same spirit as for the other three forces. Then we briefly discuss the connection between this linearized quantum gravity theory with Einstein’s nonlinear classical theory of general relativity.