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Single-particle contributions to certain classes of algebraic sum rules

Phenomenological and theoretical aspects of single-particle contributions to sum rules derived from commutation relations are considered. A derivation of sum rules arising from an equal-time axial-charge algebra evaluated between arbitrary single-particle states is given. A phenomenological analysis of these sum rules is carried out. An analogous derivation of sum rules associated with the sigma operator is shown to be invalid. An amended form for the sum rules is derived. Finally, we comment on relations obtained by taking vacuum-vacuum or vacuum-single-particle matrix elements of certain commutators.