Connection between charge conjugation, unitarity, and statistics in theories of possible small violation of the Pauli principle

It is shown that some relations among quantum field oscillators describing small violations of the Pauli exclusion principle, when generalized to local relativistic quantum fields, exhibit a connection between charge conjugation, unitarity, and statistics. The connection appears in the corresponding quantum field theories through ill-defined norm states. At the level of current algebra the value of the Schwinger term in representations of Kac-Moody and Virasoro algebras, which can be constructed from a multiflavor version of one of the field theories in two-dimensional space-time, points also to the same connection.