Document Type
Article
Publication Date
2026
Keywords
Yang-Mills equation, renormalized perturbation theory, spherical harmonics, solid harmonics, loop expansion
Abstract
This paper demonstrates convergence of the loop expansion for Yang-Mills fields.
The loop construction of perturbation theory is based on the axial gauge, ghost states, the BRST framework and the Gribov extension of the Hamiltonian, with a loop expansion cutoff to all finite orders for the dynamics.
The construction is established by renormalized perturbation theory convergent to all finite orders.
Two distinct Yang-Mills theories are constructed, one based on short distance asymptotics and the other based on long distance asymptotics.
The construction depends on an assumed principle of a maximum rate of entropy production.
The paper has sufficient generality to include existence for all cases that arise in planned future Yang-Mills studies.
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Recommended Citation
Glimm, James, "The Boson Yang-Mills Field: The Loop Expansion" (2026). Department of Applied Mathematics & Statistics Faculty Publications. 22.
https://commons.library.stonybrook.edu/ams-articles/22