W. M. Stuckey, Michael Silberstein, Timothy McDevitt
We propose a new path integral based interpretation of quantum field theory (QFT). In our interpretation, QFT is the continuous approximation of a more fundamental, discrete graph theory (theory X) whereby the Wick-rotated transition amplitude Z is a partition function constructed from boundary operators in the spacetime chain complex of the graph. Accordingly, the difference matrix and source vector of Z are related via a self-consistency criterion (SCC) based on the identity that underwrites divergence-free sources in classical field theory, i.e., the boundary of a boundary principle. The SCC ensures the source vector is divergence-free and resides in the row space of the difference matrix, which will necessarily have a non-trivial null space, so the SCC is the origin of gauge invariance. Using this formalism, we obtain the two-source transition amplitude over a (1+1)-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 (superposition and entanglement) 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. We conclude by presenting the results of our modified Regge calculus approach to Einstein-de Sitter cosmology where we produced a fit to the Union2 Compilation data for type Ia supernovae rivaling that of the concordance model ({\Lambda}CDM), but without having to invoke dark energy or accelerated expansion.
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http://arxiv.org/abs/0908.4348
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