Generalized cross-curvature symmetries in the case of non-standard gauge fields and gauge fields with energy

We consider two specific examples of non-standard gauge fields and gauge fields with energy in the presence of standard gauge fields and gauge fields with energy. We find that these models have a special relation in the gauge field theory direction of the norm of the scalar field, which is a universal symmetry of the corresponding non-standard gauge field and gauge fields with energy. We show that the corresponding quantum field theory can be realized as a class of gauge theories with gauge fields and gauge fields of the opposite energy. We then discuss some aspects of the integration and the non-perturbative limit of these theories.