The cosmological origin of the Nambu-Jona-Lasinio model

TL;DR

This paper proposes a cosmological origin for the Nambu-Jona-Lasinio model, deriving its non-linear fermion equation from gravitational interactions based on an extended Mach principle.

Contribution

It demonstrates how the Heisenberg-Nambu-Jona-Lasinio equation can emerge from gravitational interactions with the universe, extending previous scalar and spinor field models.

Findings

Derivation of NJL non-linear equation from gravity

Connection between cosmology and fermion mass generation

Extension of Mach principle to fermionic fields

Abstract

Recently a mechanism to generate mass from gravitational interaction, based on Mach principle, according to which the inertia of a body is a property of matter as well as of the background provided by the rest-of-the-universe was presented in \cite{novello} \cite{novello2}. In these papers such an idea was realized for scalar and spinor fields treating the rest-of-the-universe in its vacuum state. In the present paper, using an extended version of Mach principle, the same strategy will be applied to show how the Heisenberg-Nambu-Jona-Lasinio non-linear equation for fermions $\Psi$ arises as a consequence of the gravitational interaction of $ \Psi$ with the rest-of-the-universe.