Yang-Mills Families

Abstract

The Yang-Mills theory structure is based on group theory. It rules the symmetry relationship where the number of potential fields transforming under a same group must be equal to the number of group generators. It defines the group valued expression from where the corresponding non-abelian symmetry properties are derived.
 Nevertheless based on different origins as Kaluza-Klein, fibre bundles, supersymmetry, s-model , BRST and anti-BRST algorithm, counting degrees of freedom leads to a Yang-Mills extension under the existence of different potential fields rotating under a same single group. They establish for SU(N) the relationship where and is a flavor index, . Physically, it says that different Yang-Mills families can share a common symmetry group. They develop a whole non-abelian gauge theory.
 The effort in this work is to explore such non-abelian extension. First, to build up it on the so-called constructor basis where gauge symmetry is more available for expressing the corresponding fields strengths, Lagrangian and classical equations. After that, given that the physical fields are those associated to the poles of two-point Green functions, one derives the physical Lagrangian L written in the physical basis .
 A new physical Lagrangian associated to symmetry is generated. The meaning of Yang-Mills families appears. A symmetry of difference is realized. Where every quanta is distinguished from each other. It yields a quanta diversity associated to corresponding Yang-Mills families. There are N-spin 1 and N-spin 0 quanta separated by different quantum numbers through a whole N-dynamics. An extension to QCD becomes possible.

Non-Abelian Constructivist Lagrangian

“…Massive gluons may be helpful to solve QCD infrared problems at high energy [31][32]. Although asymptotic freedom is an achievement for quarks behaviour at deep inelastic scattering [33][34], QCD contains an incompleteness due to infrared problems at quarks and gluons scattering at high energies.…”

On Extensions of Yang-Mills-Type Theories, Their Spaces and Their Categories

“…In trying to avoiding misunderstandings, we close this section giving some non-examples in which the expression "Yang-Mills extensions" is used in a sense which is (as far as the authors know) completely unrelated with the notion introduced here: the well-known notion of supersymmetric extensions, the stringy extensions of [20], the Yang-Mills families of [15] and the extensions studied in [42].…”

“…In order to motivate our definition of extension, let us begin by noticing that in the current literature we find many ways to extend Yang-Mills theories, such as those in [27,25,8,49,50,51,52,19,22,53,42,15,20]. We note that most of them can be organized into three classes: deformations, addition of a correction term and extension of the gauge group.…”