O(5) Harmonics and Abnormal Solutions in the Bethe-Salpeter Equation

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Abstract
Exact solutions of the covariant Bethe‐Salpeter equation in the ladder approximation for two scalar particles bound by a massless particle have been obtained for all energies. By using Fock's stereographic projection, the Bethe‐Salpeter equation is transformed on to the surface of a 5‐dimensional Euclidean sphere and the solutions are then expressed as a series in O(5) harmonics. The normalization condition has been imposed by requiring that the expectation value of appropriate components of the energy‐momentum tensor with respect to the bound states is the total energy of the system; it is found that states corresponding to certain values of the quantum numbers do not satisfy the normalization requirement. These are the so‐called abnormal asolutions.

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