Hofmann provides insight into, computational tools for quantitative results on, and physics applications of quantum

Yang-Mills theory defined on a four-dimensional flat spacetime continuum.

Geometric foundations of classical

Yang-Mills theory.

Among the topics are the functoriality of Rieffel's generalized fixed-point algebras for proper actions, division algebras and supersymmetry, Riemann-Roch and index formulae in twisted K-theory, noncommutative

Yang-Mills theory for quantum Heisenberg manifolds, distances between matrix algebras that converge to coadjoint orbits, and geometric and topological structures related to M-branes.

Pure spinors as auxiliary fields in the ten-dimensional supersymmetric

Yang-Mills theory.

An Interquark qq-potential from

Yang-Mills theory has been considered in [13];

No, wait - there's still the

Yang-Mills theory, which would involve figuring out the mathematical foundation for quantum physics.

A numerical solution of the classical field equations of the

Yang-Mills theory corresponding to an infinite line of sources is presented.

Specifically, they are the Riemann hypothesis, which lingers from Hilbert's list,

Yang-Mills theory and the mass gap hypothesis, the P Versus NP problem, the Navier-Stokes equations, the Poincaire conjecture, the Birch and Swinnerton-Dyer conjecture, and the Hodge conjecture.

2021) to

Yang-Mills theory ("An extension to Maxwell's field theory that describes interactions between the weak and the strong force" [p.

In the middle volume of a three-volume set of textbooks for a series of courses that replaced the traditional course of theoretical physics, Maiani illustrates the conceptual route that led to the unification of the weak and electromagnetic interactions, starting from the identification of the weak hadronic current with the isotopic spin current; through the conserved vector current hypothesis of Fenman, Gell-Mann, and others; to

Yang-Mills theory and to the first electroweak theory of Glashow.

This work presents original research on continuum quantum geometric path integrals applied to

Yang-Mills theory and variants, such as QCD, Chern-Simons theory, and Ising Models.

Hence

Yang-Mills theory can be regarded as a theory of pure geometric objects: Q-connexion and Q-curvature with Lagrangian quadratic in curvature (as: Einstein's theory of gravitation is a theory of geometrical objects: Christoffel symbols and Riemann tensor, but with linear Lagrangian made of scalar curvature).