Journal of Rehabilitation Research Current Updates
Bordism Field Theories II: Interstitial Fields and Flux Quantization
Abstract
Ryan Jamie Buchanan and Lorenzo Rafael Flores
In this paper, we introduce interstices on warped product manifolds, which act as discrete regulators on an otherwise smooth spacetime. We analyze flux quantization and compactification in the presence of interstitial points/loci, and prove a theorem about a lemma about manifolds arising from fibered products. In order to do so, we introduce families of fields on a compactied manifold. The co-dimension of the compactification is used in our calculations to derive boundary conditions.
Our approach contributes to the literature by advancing the mathematics of string field theory, by incorporating condensed/pyknotic and ́etale mathematics, with a dash of modal logic. We begin constructing the interstices using intersections of tangent and co-tangents spaces of manifolds A and B, and generalize to tangent and co-tangent groupoids. The interstices are based spaces with a fixed locus containing a non-empty subset of Maps(T A,T∗ B). Based on these topological concepts, we propose refinements to the traditional Freund-Rubin compactification model, with new corrections arising from the cobordism structure.
Finally, we construct a new partition function for functorial TQFTs that utilizes the 4form gravitational flux, thus making this a genuine theory of quantum gravity. This work is largely speculative, but opens the door for future work on gravitational entanglement and superposition with exotic gauge fields.