The wholeness principle is analysed for non-abelian gauge symmetry. This principle states that nature acts through grouping. It says that physical laws should be derived from elds associations. At this work, we consider on the possibility of introducting a non-abelian elds set fAaIg under a common gauge parameter.A Yang-Mills extension is studied. Taking the SU(N) symmetry group with different potential elds rotating under a same group, new elds strengths are developed. They express covariant entities which are granular, collective, correlated, and not necessarily Lie algebra valued. They yield new scalars and a Lagrangian beyond Yang-Mills is obtained. Classical equations are derived and (2N + 7) equations are developed. A further step is on how such non-abelian whole symmetry is implemented at SU(N) gauge group. For this, it is studied on the algebra closure and Jacobi identities, Bianchi identities, Noether theorem, gauge xing, BRST symmetry, conservation laws, covariance, charges algebra. As result, one notices that it is installed at SU(N) symmetry independentlyon the number of involved elds. Given this consistency, Yang-Mills should not more be considered as the unique Lagrangian performed from SU(N).Introducting the BRST symmetry an invariant Leff is stablished. The BRST charge associated to the N-potential elds system is calculated and its nilpotency property obtained.Others conservations laws involving ghost scale, global charges are evalued showing that this whole symmetry extension preserve the original Yang-Mills algebra. Also the ghost number is conserved. These results imply that Yang-Mills should be understood as a pattern and not as a specic Lagrangian.Concluding, an extended Lagrangian can be constructed. It is possible to implement a non-abelian whole gauge symmetry based on a elds set fAaIg. Its physical feature is a systemic interpretation for the physical processes. Understand complexity from whole gauge symmetry.
Noether theorem for action-dependent Lagrangian functions: conservation laws for non-conservative systems
