Resolving Ordering Ambiguities in the Collective Quantization by Particle Conjugation Constraints

Abstract

We formulate the particle conjugation operation and its convenient realization as $G$--parity in the framework of several chiral soliton models. The Skyrme model, the Skyrme model with vector mesons and the chiral quark model are specifically treated. The vector and axial vector currents are classified according to their behavior under $G$--parity. In the soliton sector particle conjugation constrains {\it a priori} ambiguous orderings of operators in the space of the collective coordinates. In the Skyrme model with vector mesons and in a local chiral model with an explicit valence quark this classification scheme provides consistency conditions for the ordering of the collective operators appearing in the $1/N_C$ corrections to the nucleon axial charge and the isovector magnetic moment. These consistency conditions cause the corrections obtained from an ordinary perturbation expansion to vanish in the context of the collective quantization of the static soliton configuration. This conclusion presumably applies to all local effective chiral models.