Abstract
The possible transformation properties of the energy operator under the chiral SU 3 × SU 3 algebra are investigated, assuming that it transforms as a singlet and the eighth component of an octet under SU 3 and has certain simple transformation properties under the non-strange chiral SU 2 × SU 2. It is shown that the SU 2 × SU 2 invariant part of the energy operator can only belong to the representations (1,8) + (8,1) and (3,3 ∗) + (3 ∗,3) of SU 3 × SU 3, 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 SU 2 × SU 2 (i.e. the pion σ-terms are isoscalar), we find its possible SU 3 × SU 3 transformation properties.
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