Chiral Perturbation Theory in the Framework of Non-Commutative Geometry

TL;DR

This paper develops a non-commutative geometric extension of chiral perturbation theory, constraining coupling constants and successfully reproducing key terms in the Skyrme model, aligning well with experimental data.

Contribution

It introduces a non-commutative framework for chiral perturbation theory, providing new insights and reproducing important model terms with correct coefficients.

Findings

Coupling constants are tightly constrained and match data.

Reproduces the non-Skyrme term in the Skyrme model accurately.

Comments on a similar approach for the linear sigma model.

Abstract

We consider the non-commutative generalization of the chiral perturbation theory. The resultant coupling constants are severely restricted by the model and in good agreement with the data. When applied to the Skyrme model, our scheme reproduces the non-Skyrme term with the right coefficient. We comment on a similar treatment of the linear $\sigma $-model.