It is shown in a simple model that physical masses can split even without particle mixture in a Hamiltonian in which bare masses are degenerate and permutation symmetry holds among bare particles. Infinity of the normalization volume is indispensable for proof. In its connection the problem of representation of an operator ring is discussed. A model of quantum number non-conservation is briefly considered in the same spirit.
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Mahiko Suzuki (1963) studied this question.