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.

20 pages LaTeX, Conclusions made more precise, some recent references added

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Cited by in corpus (7)

• Polarized Nucleon Structure Functions within a Chiral Soliton Model
• Light-flavor sea-quark distributions in the nucleon in the SU(3) chiral quark soliton model (I) -- phenomenological predictions --
• The generalized parton distribution functions and the nucleon spin sum rules in the chiral quark soliton model
• The Constituent Quark Limit and the Skyrmion Limit of the Chiral Quark Soliton Model
• Light-flavor sea-quark distributions in the nucleon in the SU(3) chiral quark soliton model (II) -- theoretical formalism --
• Magnetic Moments of the SU(3) Octet Baryons in the semibosonized SU(3) Nambu-Jona-Lasinio Model
• Nucleon Structure Functions in the Three Flavor NJL Soliton Model