### Abstract:

We have established that SU(N) symmetry group generators occur in a spectrum with a
quantum structure composed of N − 1 configuration shells each containing a definite number of
symmetric and antisymmetric pairs of generators specified by quantum numbers l = 1, ..., N − 1
; m = 0, 1, ..., l. Interpreting the generators as spin angular momentum operators brings the generator spectrum to a form precisely similar to the spectrum of orbital angular momentum states
composed of orbital configuration shells containing definite numbers of orbital states specified
by orbital and magnetic quantum numbers l = 0, 1, ..., n − 1 ; m = 0, ±1, ..., ±l in the n
th-energy
level of an atom, thus revealing that the quantum state space of an SU(N) symmetry group
corresponds directly to the quantum state space of the n
th-energy level of an atom. Within each
configuration shell containing specified generators in the SU(N) generator spectrum, we have
determined the associated quadratic and Fubini-Veneziano spin angular momentum operators to
general order, which we have finally used to obtain the corresponding universal SU(N) quadratic
and Fubini-Veneziano spin operators. Basic algebraic relations of the resulting Cartan-Weyl
generators have been determined explicitly for general SU(N) symmetry groups. Considering
applications to gauge field theories, we easily establish that SU(N) gauge fields have quantum
structure corresponding directly to the SU(N) generator spectrum. We have provided elaborate
explanations of the important implications of the expanded algebraic properties and quantum
structure of the SU(N) generator spectrum to the existing SU(N) gauge field theories.