The Regge Pole Behavior of Extended Particles

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Abstract
An extended particle is described on the basis of the Regge pole hypothesis. The internal structure is specified as a realization of the Lorentz group over all the region of the outer four-momentum Pµ, being characterized by the complex spin angular momentum α(P2µ) dependent on P2µ. Similarly, the unitary spin is conjectured to be derived from the internal space-time structure of an extended particle. The corresponding internal structure is also specified group-theoretically over all the region of the four-momentum by the complex values of Casimir invariants of the Reggeized unitary symmetry group, ν(P2µ)'s dependent on P2µ. These “Regge trajectories” α(P2µ) and ν(P2µ)'s are considered to be determined by basic equations for an extended particle which relate the outer four-momentum to the internal structure. Nonlocal interactions between extended particles are almost uniquely determined by virtue of the group-theoretical characterization of the internal structure. The complex generalization of unitary spin leads one naturally to a result of the broken symmetry.

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