Bilocal wave equation for baryons lying on linear trajectories and its extension to a linear chain model

A new bilocal wave equation for baryonic states is presented. It is a first-order differential equation containing three independent Dirac matrices, one of which is associated to the internal extension. The presence of three Dirac matrices assimilates three quark spins. The wave equation represents baryonic states lying on parallel linear trajectories. From the requirement for the existence of conserved current the model predicts that the intercept of the leading trajectory should be less than 1/2, in accord with observation. The corresponding bilocal theory for mesons requiring the introduction of two independent Dirac matrices is stated briefly. The generalization to the linear multilocal case which represents a one-dimensional chain consisting on N discrete points is performed and is analysed by the aid of normal mode expansion. The strong and electromagnetic interactions can be introduced to the model, though the theory is still at the non-second-quantized level. In the limit N → ∞ the chain model goes over to the "double Dirac string model" which is relevant to derivation of the dual amplitude, and this limiting transition from the discrete to the continuous case clarifies the boundary conditions and other subtleties for the latter model.