Reggeization of U(6)⊗U(6)

Assuming U(6)⊗U(6) invariance of the S matrix in the center-of-mass system, we postulate a meromorphy of the physical amplitude in the Casimir plane of U(6)⊗U(6) for a generalized partial-wave analysis. These poles in the S matrix correspond to generalized Regge trajectories, and physically to sequences of U(6)⊗U(6) particle multiplets. The paper is concerned with detailed specification of different types of trajectories that may arise; these correspond to the ten types of unitary representation of the cross-channel continuation of the rest-symmetry group to GL(6,C) in which up to six Casimir operators are made complex. A particularly simple case is the Reggeization of the quark number which provides the degenerate sequence of U(6)⊗U(6) states. For this series we compute the generalized rotation functions. The Reggeization of quark number denudes this number of any fundamental physical meaning; quarks are simply excitation modes.