Bi-Local Higgs-Like Fields Based on Non-Commutative Geometry

TL;DR

This paper explores a non-commutative geometric framework for bi-local hadron models, revealing Higgs-like fields as connectors between spacetime points and linking meson duality to chiral symmetry breaking.

Contribution

It introduces a novel non-commutative geometric approach to bi-local hadron models, connecting Higgs-like fields with meson duality and chiral symmetry breaking.

Findings

Higgs-like scalar fields act as bridges between spacetime points.

The action resembles the linear sigma model.

Meson fields are dual to Nambu-Goldstone bosons.

Abstract

The bi-local model of hadrons is studied from the viewpoint of non-commutative geometry formulated so that Higgs-like scalar fields play the role of a bridge, the bi-local fields, connecting different spacetime points. We show that the resultant action for Higgs-like scalar fields has a structure similar to that of the linear sigma model. According to this formalism, we can deduce the dual nature of meson fields as the Nambu-Goldstone bosons associated with chiral symmetry breaking and bound states of quarks.