A unitary transformation, which plays the same role as the Foldy transformation in the pion-nucleon system, is constructed for the case where the pion interacts with both $\Sigma$ and $\Lambda$ hyperons through ${\gamma }_5$ couplings. The transformation function and the transformed Hamiltonian are very similar to those of the Foldy transformation, in spite of the complexity of our system in isotopic spin space. The application to practical problems is not considered in this paper.

• Received 15 December 1959

DOI:https://doi.org/10.1103/PhysRev.118.1664