Yang-Mills theories

There is a vast literature on the subject of the two-dimensional Yang-Mills theory, approaching it from different points of view. One of the latest papers is... 

There are many important and interesting aspects in two-dimensional Yang-Mills theory. One of them is the issue of determination of physical observables Wilson loops [Eq. (8)]. Calculation of the Wilson loops WR(C) in two-dimensional Yang-Mills theory can be facilitated by the use of the non-Abelian Stokes theorem. 

N. E. Bralic, Exact Computation of Loop Averages in Two Dimensional Yang-Mills theory,... 

There exist generally covariant four-valued 4-vectors that are components of q, and these can be used to construct the basic structure of 0(3) electrodynamics in terms of single-valued components of the quaternion-valued metric q1. Therefore, the Sachs theory can be reduced to 0(3) electrodynamics, which is a Yang-Mills theory [3,4]. The empirical evidence available for both the Sachs and 0(3) theories is summarized in this review, and discussed more extensively in the individual reviews by Sachs [1] and Evans [2]. In other words, empirical evidence is given of the instances where the Maxwell-Heaviside theory fails and where the Sachs and 0(3) electrodynamics succeed in describing empirical data from various sources. The fusion of the 0(3) and Sachs theories provides proof that the B(3) held [2] is a physical held of curved spacetime, which vanishes in hat spacetime (Maxwell-Heaviside theory [2]). 

In Eq. (5), the product q q is quaternion-valued and non-commutative, but not antisymmetric in the indices p and v. The B<3> held and structure of 0(3) electrodynamics must be found from a special case of Eq. (5) showing that 0(3) electrodynamics is a Yang-Mills theory and also a theory of general relativity [1]. The important conclusion reached is that Yang-Mills theories can be derived from the irreducible representations of the Einstein group. This result is consistent with the fact that all theories of physics must be theories of general relativity in principle. From Eq. (1), it is possible to write four-valued, generally covariant, components such as... 

Since 0(3) electrodynamics is a Yang-Mills theory [3,4], we can write... 

All topological theories are nonlinear, a feature of both the Sachs and Evans theories, and the whole of quantum theory can be replaced by topology [1], which reduces in some circumstances to the Yang-Mills theory [1], of which 0(3) electrodynamics [3] is an example. 0(3) electrodynamics has been developed into an 0(3) symmetry quantum field theory by Evans and Crowell... 

There are therefore obvious points of similarity between the 0(3) theory of electrodynamics and the Yang-Mills theory [44], Both are based, as we have argued, on an 0(3) or SU(2) invariant Lagrangian. However, in 0(3) electrodynamics, the particle concomitant with the field has the topological charge k/A(0>. In 0(3) electrodynamics, the internal space and spacetime are not independent spaces but form an extended Lie algebra [42], In elementary particle... 

Here we mean the kind of groups addressed in Yang-Mills theory, which are continuous groups (as opposed to discrete groups). Unlike discrete groups, continuous groups contain an infinite number of elements and can be differentiable or analytical [1],... 

It is reasonable... to ask for the determination of the classical field configurations in Euclidean space which minimize the action, subject to appropriate asymptotic conditions in 4-space. These classical solutions are the instantons of the Yang-Mills theory. 

R. Jackiw, C. Nohl, and C. Rebbi, Classical and Semi-classical Solutions to Yang-Mills Theory (Proc. Banff School), Plenum, 1977. 

Non-Abelian local gauge invariance—Yang-Mills theories... 

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