Abstract

We propose a new path integral based interpretation of quantum field theory. In our interpretation, QFT is the continuous approximation of a more fundamental, discrete graph theory whereby the transition amplitude Z is not viewed as a sum over all paths in configuration space, but measures the symmetry of the differential operator and source vector of the discrete graphical action. We propose that the differential operator and source vector of theory X are related via a self-consistency criterion based on the identity that underwrites divergence-free sources in classical field theory, i.e., the boundary of a boundary principle. In this approach, the SCC ensures the source vector is divergence-free and resides in the row space of the differential operator. Accordingly, the differential operator will necessarily have a non-trivial eigenvector with eigenvalue zero, so the SCC is the origin of gauge invariance. Factors of infinity associated with gauge groups of infinite volume are excluded in our approach, since Z is restricted to the row space of the differential operator and source vector. We show it is possible that the underlying theory X, despite being discrete, is the basis for exact Poincaré invariance. Using this formalism, we obtain the two-source transition amplitude over a -dimensional graph with N vertices fundamental to the scalar Gaussian theory and interpret it in the context of the twin-slit experiment to provide a unified account of the Aharonov-Bohm effect and quantum non-separability that illustrates our ontic structural realist alternative to problematic particle and field ontologies. Our account also explains the need for regularization and renormalization, explains gauge invariance and largely discharges the problems of inequivalent representations and Haag’s theorem. This view suggests corrections to general relativity via modifications to its graphical counterpart, Regge calculus. We conclude by presenting the results of our modified Regge calculus approach to Einsteinde Sitter cosmology where we produced a fit to the Union2 Compilation data for type Ia supernovae rivaling that of the concordance model, but without having to invoke dark energy or accelerated expansion.