Document Type
Article
Publication Date
2026
Keywords
Yang-Mills, Fermion Sign Problem, entropy, renormalized perturbation theory, spherical harmonics, solid harmonics
Abstract
Quantum Yang-Mills fields are constructed.
The Fermion sign problem is addressed through the theory of homology groups and thimbles. The sign problem for residual states not reached by the homology groups and thimbles is resolved by a perturbative expansion which is shown to be convergent to all finite orders.
The Fermion doubling problem is avoided through consideration of vacuum expectation values, where it does not exist.
The proofs depend on an assumed principle of a maximum rate of entropy production.
Two Yang-Mills gauge field theories are constructed, one based on short distance asymptotics and the other based on long distance asymptotics.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Glimm, James, "The Yang Mills Field, I: Existence" (2026). Department of Applied Mathematics & Statistics Faculty Publications. 14.
https://commons.library.stonybrook.edu/ams-articles/14