Abstract
In certain molecular models, and related one-dimensional field theories, localized objects appear with half-integral expectation values of charge. We consider whether these states are eigenstates of charge, with half-integral eigenvalue. We find that it is indeed so for a suitably diffuse definition of the charge operator in question. This diffuse charge operator has a spectrum which approaches a continuum. The analysis is made on a lattice, to avoid divergence ambiguities, and on a finite length, which is only subsequently made large. The half-integral charge phenomenon is not tied to solitons, but can also arise as an end effect.
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