Document Type
Article
Publication Date
2026
Keywords
Renormalized Perturation Theory, Scaling to all orders, intermediate asymptotics, change of covariance group
Abstract
A mathematically rigorous renormalized perturbative expansion, truncated to all finite orders, establishes the existence of quantum general relativity theories with Fermion matter fields. The expansion is initialized with the selection of a vacuum state. Distinct infrared (IR) and ultraviolet (UV) vacuum states are considered. The IR vacuum state defines a cosmology model. The UV vacuum state defines a black hole model. The vacuum state is initialized with a o3 gauge Lie algebra defining a quark-gluon plasma. With this choice, string theory is avoided. Finite order renormalized perturbation theory, defined using Bosons to avoid Fermion sign cancellation, is convergent to all finite orders and in the dual Schwartz space S′. The sign problem for evaluation of Fermion correlation functions is resolved with the aid of the Boson perturbative expansion, truncated to all finite orders. Once resolved, the full Fermion perturbation expansion is also convergent to all finite orders. The perturbative construction is based on the Riemann tensor, the Einstein equation conservation of energy and mass and the Gribov extension of the Lagrangian, within a loop expansion convergent to all finite orders for the dynamics. The construction employs an assumed principle of a maximum rate of entropy production.
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Recommended Citation
Glimm, James, "Scaling Laws" (2026). Department of Applied Mathematics & Statistics Faculty Publications. 20.
https://commons.library.stonybrook.edu/ams-articles/20