Abstract
The relations between unitary and permutation groups are well known 1). Some time ago, Yamaguchi has constructed 2) a model showing that invariance under all permutations of three “chaos” fields and a Fermi type Hamiltonian for the “physical” fields lead to a U (2) invariant theory, if there are in addition enough additive conservation laws. This model was generalized by Schechter et al. 3), who have shown, without any restriction on the interaction, that two additive conservation laws and permutation invariance yield generally U(3) invariance. In this letter we refine this last result and show that one additive conservation law, permutation and “ I invariance” lead to a U(3) invariant theory. Furthermore the case of four fundamental fields, is briefly investigated.
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