Extend holographic mixing framework to non-Abelian gauge fields

Extend the holographic mixing and Fock space dynamics developed for abelian gauge fields in causal fermion systems to encompass non-Abelian gauge fields, formulating the corresponding operator structures, commutation relations, and dynamical equations.

Background

The paper derives abelian gauge dynamics (QED) as a limiting case. Generalizing to non-Abelian interactions would broaden the applicability of the framework and is highlighted by the authors as an unresolved challenge.

Such an extension would require adapting the stochastic field modeling, holographic phases, and operator algebra to the non-Abelian setting.