Huygens-Fresnel Principle in Superspace

Abstract

We first roughly present a summary of the optico-mechanical analogy, which has always been so profitable in physics. Then we put forward a geometrodynamical formulation of gravity suitable to our intentions, both formally and conceptually. We present difficulties in some approaches to canonically quantize gravity which can be amended by the idea put forward in this paper, which we introduce in the last section. It consists basically in trying to find an intermediary between the quantization step going from the classical superhamiltonian constraint to the Wheeler-DeWitt equation. This is accomplished by inputting interference beyond the WKB approximation, through a type of Huygens-Fresnel Principle (HFP) in superspace.