The classic question of a nonabelian Yang-Mills analogue to electromagnetic duality is here examined in a minimalist fashion at the strictly 4-dimensional, classical field and point charge level. A generalisation of the abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the abelian theory. For example, there is ...

We introduce a method that generates invariant functions from classical field theories depending on external parameters. We apply our method to several field theories such as abelian BF , Chern-Simons and 2-dimensional Yang-Mills theory.

Yang-Mills Theories [1, 2, 3, 4] play an important hole on the description of both strong and weak interactions, being one of the most successful pillars of Fundamental Interactions. Nowadays electromagnetic and gravitational interactions can also be systematically described by the mechanisms of this class of field theories [5, 6, 7]. Here we develop a different approach to derive from classica...

In generalized Yang-Mills theories scalar fields can be gauged just as vector fields in a usual Yang-Mills theory, albeit it is done in the spinorial representation. The presentation of these theories is aesthetic in the following sense: A physical theory using Yang-Mills theories requires several terms and irreducible representations, but with generalized Yang-Mills theories, only two terms an...

symbol or equation Corresponding expression for the Yang-Mills field Corresponding expression for the gravitational field p=0, 1,2,3 n=1 ~ ~ n Ppv=gfsv 'QIbv j P&v =Op1p2p3b Ppy= Pv F P @vs7 S— = g'" &'&m~,

A gauge-invariant field is found which describes physical configurations, i.e. gauge orbits, of non-Abelian gauge theories. This is accomplished with non-Abelian generalizations of the Poincaré-Hodge decomposition formula for one-forms. In a particular sense, the new field is dual to the gauge field. Using this field as a coordinate, the metric and Riemann curvature are discussed for Yang-Mills...

The large-N limit of the quantum Yang-Mills field over the plane R2, for the gauge group U(N), is shown to lead to a white noise field in the sense of free probability.

This paper develops the Riemannian geometry of classical gauge theories Yang-Mills fields coupled with scalar and spinor fields on compact four-dimensional manifolds. Some important properties of these fields are derived from elliptic theory : regularity, an "energy gap theorem", the manifold structure of the configuration space, and a bound for the supremum of the field in terms of the energy....