An exciting fundamental derivation of SU(3) and a simultaneos lyemerging derivation of SU(6) all just from space-time symmetry

We utilize Foldy's canonical representation (m,5/2) + -m,5/2) involving degrees of freedom pertaining to a spin of 5/2 units and make a unitary transformation to the current picture thereby deriving an expressing for the total angular momentum consisting of a together conserved orbital plus an intrinsic spin -1/2 part and yet another separately conserved SU(3)-unitary spin part. We demonstrate this explicity by algebraically deducing the Cartan-Weyl basis for The newly emerging invariance algebra whose eight generators are expressed in terms of three fundamental matrices representing spin-5/2 and proving that this basis excitingly coincides with that of the SU(3) algebra. The derivation of SU(6) in automatically achieved in our theory as a materials consequence Of the SU(3)-symmetry already derived and an SU(2)-spin symmetry guaranteed by the commentativity of Foldys mean sprin operators that find their find their natural places in the unitary-spin parts of the expressions for the Poincare generators, with the Dirac-type hamiltonian acting as the time-transtation generator. As a prelude aderivation of SU(2) is, initially presented working with Foldy's canomical representation (m,3/2) + (-m,3/2). In the process of deriving SU(2), an invariance under the discrete symmetrIc group S3 is also simultaneously datained. (author)