Operator Formalism for Daughter Trajectories in the Bethe-Salpeter Equation

The existence of daughter Regge poles is demonstrated by a raising and lowering operator formalism without explicit use of $O\left(4\right)\mathrm{}$ symmetry. The commutation relations of these operators with the kernel of the Bathe-Salpeter integral equation require the existence of the degeneracy which leads to an infinite chain of daughter Regge trajectories. It is found that the chain of daughter poles does not terminate even if the parent pole is at a positive integer. A formula is given for calculating the slopes of the Regge trajectories.