W Spin for Any Spin

The collinear group SU(6)w enables us to discuss vertices, form factors and other collinear processes in an SU(6)-theory which is consistent with relativistic invariance. It leads, however, to a classification of the particles which is different from that of the “staticL SU(6)s. The general “W-spin” properties of an arbitrary spin state constructed from any number of basic spin i objects are discussed in detail. Explicit formulae for expressing the eigenstates of s2 as linear combinations of ordinary spin states are given and some properties of the transformation matrices are discussed. The relation between W-spin and ordinary S-spin in the framework of the SU(2) @ SU(2) algebra is generalized to an arbitrary Lie algebra of the form G :@I G. Some examples of such generalized W-type algebras are considered and the special case of SU(6)w and SU(6)s is discussed in detail. An explicit formula for calculating the SU(6)W properties of an arbitrary component of a representation of the non-chiral U( 6) (3 U(6) is given. Some explicit transformation matrices between the eigenstates of W-spin and S-spin are given in the appendix.