Emergence of Yang Mills theory from the Non-Abelian Nambu Model

TL;DR

This paper proves the equivalence between the Non-Abelian Nambu Model and Yang Mills theory, showing that Lorentz violation in NANM is unobservable and Goldstone bosons correspond to gauge fields.

Contribution

It demonstrates the equivalence of NANM and Yang Mills theory under certain conditions, clarifying the physical role of Lorentz violation and Goldstone bosons.

Findings

NANM and Yang Mills are equivalent when Gauss laws are imposed.

Lorentz violation in NANM is physically unobservable.

Goldstone bosons in NANM are identified as gauge fields.

Abstract

The equivalence between the Non-Abelian Nambu model (NANM) and Yang Mills theory is proved, after demanding the Gauss laws at some initial time to the first one. Thereby, the Lorentz violation encoded into the constraint that defines the NANM is physically unobservable. As result, the Goldstone bosons in the NANM arising from the spontaneous symmetry breaking can be identified as the standard gauge fields.