ON BREAKIND OF SU3XSU3 SYMMETRY

The possible transformation properties of the energy operator under the chiral SU3 × SU3 algebra are investigated, assuming that it transforms as a singlet and the eighth component of an octet under SU3 and has certain simple transformation properties under the non-strange chiral SU2 × SU2. It is shown that the SU2 × SU2 invariant part of the energy operator can only belong to the representations (1,8) + (8,1) and (3,3*) + (3*,3) of SU3 × SU3, as suggested by Gell-Mann, Oakes and one of the authors. Making the further assumption that the remaining part of the energy operator belongs to a four-dimensional multiplet under the non-strange chiral SU2 × SU2 (i.e. the pion σ-terms are isoscalar), we find its possible SU3 × SU3 transformation properties. © 1969.